Circles Questions

MathematicsCircles106 Questions Found

MathematicsStandard and General Equation of a CircleJEE Advanced 1983Easy

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The points of intersection of the line $4 x - 3 y - 10 = 0$ and the circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0$ are ......... and .........

Answer:(4, 2), (-2, -6)

MathematicsStandard and General Equation of a CircleJEE Advanced 1984Easy

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The abscissa of the two points $A$ and $B$ are the roots of the equation $x^{2} + 2 a x - b^{2} = 0$ and their ordinates are the roots of the equation $x^{2} + 2 p x - q^{2} = 0$ . Find the equation and the radius of the circle with $A B$ as diameter.

Answer:x^2 + y^2 + 2ax + 2py - b^2 - q^2 = 0, \sqrt{a^2 + p^2 + b^2 + q^2}

MathematicsEquation of Tangent and NormalJEE Advanced 1985Moderate

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From the origin chords are drawn to the circle $(x - 1)^{2} + y^{2} = 1$ . The equation of the locus of the mid-points of these chords is .........

Answer:x^2 + y^2 - x = 0

MathematicsStandard and General Equation of a CircleJEE Advanced 1986Moderate

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Lines $5 x + 12 y - 10 = 0$ and $5 x - 12 y - 40 = 0$ touch a circle $C_{1}$ of diameter 6. If the centre of $C_{1}$ lies in the first quadrant, find the equation of the circle $C_{2}$ which is concentric with $C_{1}$ and cuts intercepts of length 8 on these lines.

Answer:x^2 + y^2 - 10x - 4y + 4 = 0

MathematicsStandard and General Equation of a CircleJEE Advanced 1986Moderate

View in:English Hindi

From the point $A (0, 3)$ on the circle $x^{2} + 4 x + (y - 3)^{2} = 0$ , a chord $A B$ is drawn and extended to a point $M$ such that $A M = 2 A B$ . The equation of the locus of $M$ is .........

Answer:x^2 + y^2 + 8x - 6y + 9 = 0

MathematicsDirector Circle and Family of CirclesJEE Advanced 1986Easy

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The equation of the line passing through the points of intersection of the circles $3 x^{2} + 3 y^{2} - 2 x + 12 y - 9 = 0$ and $x^{2} + y^{2} + 6 x + 2 y - 15 = 0$ is .........

Answer:10x - 3y - 18 = 0

MathematicsLength of Tangent and Chord of ContactJEE Advanced 1988Moderate

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If the circle $C_{1} : x^{2} + y^{2} = 16$ intersects another circle $C_{2}$ of radius 5 in such a manner that common chord is of maximum length and has a slope equal to $3/4$ , then the coordinates of the centre of $C_{2}$ are .........

Answer:(-9/5, 12/5) or (9/5, -12/5)

MathematicsEquation of Tangent and NormalJEE Advanced 1989Easy

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The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $x^{2} + y^{2} = 4$ at $(1, rac{\sqrt{3}}{1})$ is .........

Answer:2\sqrt{3}

MathematicsEquation of Tangent and NormalJEE Advanced 1990Difficult

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A circle touches the line $y = x$ at a point $P$ such that $O P = 42$ , where $O$ is the origin. The circle contains the point $(- 10, 2)$ in its interior and the length of its chord on the line $x + y = 0$ is $62$ . Determine the equation of the circle.

Answer:x^2 + y^2 + 18x - 2y + 32 = 0

MathematicsEquation of Tangent and NormalJEE Advanced 1991Moderate

View in:English Hindi

Two circles, each of radius 5 units, touch each other at $(1, 2)$ . If the equation of their common tangent is $4 x + 3 y = 10$ , find the equation of the circles.

Answer:x^2 + y^2 + 6x + 2y - 15 = 0 \text{ and } x^2 + y^2 - 10x - 10y + 25 = 0

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The points of intersection of the line 4x−3y−10=0 and the circle x2+y2−2x+4y−20=0 are ......... and .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } From the origin chords are drawn to the circle (x−1)2+y2=1. The equation of the locus of the mid-points of these chords is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } From the point A(0,3) on the circle x2+4x+(y−3)2=0, a chord AB is drawn and extended to a point M such that AM=2AB. The equation of the locus of M is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The equation of the line passing through the points of intersection of the circles 3x2+3y2−2x+12y−9=0 and x2+y2+6x+2y−15=0 is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle x2+y2=4 at (1, rac{\sqrt{3}}{1}) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two circles, each of radius 5 units, touch each other at (1,2). If the equation of their common tangent is 4x+3y=10, find the equation of the circles.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The points of intersection of the line 4x−3y−10=0 and the circle x2+y2−2x+4y−20=0 are ......... and .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } From the origin chords are drawn to the circle (x−1)2+y2=1. The equation of the locus of the mid-points of these chords is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } From the point A(0,3) on the circle x2+4x+(y−3)2=0, a chord AB is drawn and extended to a point M such that AM=2AB. The equation of the locus of M is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The equation of the line passing through the points of intersection of the circles 3x2+3y2−2x+12y−9=0 and x2+y2+6x+2y−15=0 is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle x2+y2=4 at (1, rac{\sqrt{3}}{1}) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two circles, each of radius 5 units, touch each other at (1,2). If the equation of their common tangent is 4x+3y=10, find the equation of the circles.

The points of intersection of the line $4 x - 3 y - 10 = 0$ and the circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0$ are ......... and .........

From the origin chords are drawn to the circle $(x - 1)^{2} + y^{2} = 1$ . The equation of the locus of the mid-points of these chords is .........

From the point $A (0, 3)$ on the circle $x^{2} + 4 x + (y - 3)^{2} = 0$ , a chord $A B$ is drawn and extended to a point $M$ such that $A M = 2 A B$ . The equation of the locus of $M$ is .........

The equation of the line passing through the points of intersection of the circles $3 x^{2} + 3 y^{2} - 2 x + 12 y - 9 = 0$ and $x^{2} + y^{2} + 6 x + 2 y - 15 = 0$ is .........

The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $x^{2} + y^{2} = 4$ at $(1, rac{\sqrt{3}}{1})$ is .........

Two circles, each of radius 5 units, touch each other at $(1, 2)$ . If the equation of their common tangent is $4 x + 3 y = 10$ , find the equation of the circles.

The points of intersection of the line $4 x - 3 y - 10 = 0$ and the circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0$ are ......... and .........

From the origin chords are drawn to the circle $(x - 1)^{2} + y^{2} = 1$ . The equation of the locus of the mid-points of these chords is .........

From the point $A (0, 3)$ on the circle $x^{2} + 4 x + (y - 3)^{2} = 0$ , a chord $A B$ is drawn and extended to a point $M$ such that $A M = 2 A B$ . The equation of the locus of $M$ is .........

The equation of the line passing through the points of intersection of the circles $3 x^{2} + 3 y^{2} - 2 x + 12 y - 9 = 0$ and $x^{2} + y^{2} + 6 x + 2 y - 15 = 0$ is .........

The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $x^{2} + y^{2} = 4$ at $(1, rac{\sqrt{3}}{1})$ is .........

Two circles, each of radius 5 units, touch each other at $(1, 2)$ . If the equation of their common tangent is $4 x + 3 y = 10$ , find the equation of the circles.