Straight Lines Questions

MathematicsStraight Lines102 Questions Found

MathematicsVarious Forms of Equations of a LineJEE Advanced 1980Easy

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A straight line $L$ is perpendicular to the line $5 x - y = 1$ . The area of the triangle formed by the line $L$ and the coordinate axes is 5. Find the equation of the line $L$ .

Answer:x + 5y - 5\sqrt{2} = 0 \text{ or } x + 5y + 5\sqrt{2} = 0

MathematicsFamily of LinesJEE Advanced 1982Easy

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The set of lines $a x + b y + c = 0$ , where $3 a + 2 b + 4 c = 0$ is concurrent at the point .........

Answer:

(3/4, 1/2)

MathematicsArea of TriangleJEE Advanced 1983Easy

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The coordinates of $A, B, C$ are $(6, 3)$ , $(- 3, 5)$ , $(4, - 2)$ respectively, and $P$ is any point $(x, y)$ . Show that the ratio of the area of the triangles $△ P B C$ and $△ A B C$ is $∣ \frac{x + y - 2}{7} ∣$ .

Answer:|\frac{x+y-2}{7}|

MathematicsCentroid, Incenter, Orthocenter, and CircumcenterJEE Advanced 1983Moderate

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The vertices of a triangle are $[a t_{1} t_{2}, a (t_{1} + t_{2})]$ , $[a t_{2} t_{3}, a (t_{2} + t_{3})]$ , $[a t_{3} t_{1}, a (t_{3} + t_{1})]$ . Find the orthocentre of the triangle.

Answer:(-a, a(t_1 + t_2 + t_3) + at_1t_2t_3)

MathematicsVarious Forms of Equations of a LineJEE Advanced 1983Moderate

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The end $A, B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $O X, O Y$ respectively. If the rectangle $O A P B$ be completed, then show that the locus of the foot of the perpendicular drawn from $P$ to $A B$ is $x^{2/3} + y^{2/3} = c^{2/3}$ .

Answer:x^{2/3} + y^{2/3} = c^{2/3}

MathematicsAngle Between Two LinesJEE Advanced 1984Moderate

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Two equal sides of an isosceles triangle are given by the equations $7 x - y + 3 = 0$ and $x + y - 3 = 0$ and its third side passes through the point $(1, - 10)$ . Determine the equation of the third side.

Answer:x - 3y - 31 = 0 \text{ or } 3x + y + 7 = 0

MathematicsFamily of LinesJEE Advanced 1984Easy

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If $a, b$ and $c$ are in A.P., then the straight line $a x + b y + c = 0$ will always pass through a fixed point whose coordinates are .........

Answer:

(1, - 2)

MathematicsAngle Between Two LinesJEE Advanced 1985Moderate

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Two sides of a rhombus $A B C D$ are parallel to the lines $y = x + 2$ and $y = 7 x + 3$ . If the diagonals of the rhombus intersect at the point $(1, 2)$ and the vertex $A$ is on the y-axis, find possible co-ordinates of $A$ .

Answer:(0, 0) \text{ or } (0, 5/2)

MathematicsCentroid, Incenter, Orthocenter, and CircumcenterJEE Advanced 1985Moderate

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The orthocentre of the triangle formed by the lines $x + y = 1, 2 x + 3 y = 6$ and $4 x - y + 4 = 0$ lies in quadrant number .........

Answer:first quadrant

MathematicsFamily of LinesJEE Advanced 1988Moderate

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Lines $L_{1} \equiv a x + b y + c = 0$ and $L_{2} \equiv l x + m y + n = 0$ intersect at the point $P$ and make an angle $θ$ with each other. Find the equation of a line $L$ different from $L_{2}$ which passes through $P$ and makes the same angle $θ$ with $L_{1}$ .

Answer:(a^2 + b^2)(lx + my + n) - 2(al + bm)(ax + by + c) = 0

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A straight line L is perpendicular to the line 5x−y=1. The area of the triangle formed by the line L and the coordinate axes is 5. Find the equation of the line L.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The set of lines ax+by+c=0, where 3a+2b+4c=0 is concurrent at the point .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The vertices of a triangle are [at1​t2​,a(t1​+t2​)], [at2​t3​,a(t2​+t3​)], [at3​t1​,a(t3​+t1​)]. Find the orthocentre of the triangle.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a,b and c are in A.P., then the straight line ax+by+c=0 will always pass through a fixed point whose coordinates are .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x−y+4=0 lies in quadrant number .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A straight line L is perpendicular to the line 5x−y=1. The area of the triangle formed by the line L and the coordinate axes is 5. Find the equation of the line L.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The set of lines ax+by+c=0, where 3a+2b+4c=0 is concurrent at the point .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The vertices of a triangle are [at1​t2​,a(t1​+t2​)], [at2​t3​,a(t2​+t3​)], [at3​t1​,a(t3​+t1​)]. Find the orthocentre of the triangle.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a,b and c are in A.P., then the straight line ax+by+c=0 will always pass through a fixed point whose coordinates are .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x−y+4=0 lies in quadrant number .........

A straight line $L$ is perpendicular to the line $5 x - y = 1$ . The area of the triangle formed by the line $L$ and the coordinate axes is 5. Find the equation of the line $L$ .

The set of lines $a x + b y + c = 0$ , where $3 a + 2 b + 4 c = 0$ is concurrent at the point .........

The vertices of a triangle are $[a t_{1} t_{2}, a (t_{1} + t_{2})]$ , $[a t_{2} t_{3}, a (t_{2} + t_{3})]$ , $[a t_{3} t_{1}, a (t_{3} + t_{1})]$ . Find the orthocentre of the triangle.

If $a, b$ and $c$ are in A.P., then the straight line $a x + b y + c = 0$ will always pass through a fixed point whose coordinates are .........

The orthocentre of the triangle formed by the lines $x + y = 1, 2 x + 3 y = 6$ and $4 x - y + 4 = 0$ lies in quadrant number .........

A straight line $L$ is perpendicular to the line $5 x - y = 1$ . The area of the triangle formed by the line $L$ and the coordinate axes is 5. Find the equation of the line $L$ .

The set of lines $a x + b y + c = 0$ , where $3 a + 2 b + 4 c = 0$ is concurrent at the point .........

The vertices of a triangle are $[a t_{1} t_{2}, a (t_{1} + t_{2})]$ , $[a t_{2} t_{3}, a (t_{2} + t_{3})]$ , $[a t_{3} t_{1}, a (t_{3} + t_{1})]$ . Find the orthocentre of the triangle.

If $a, b$ and $c$ are in A.P., then the straight line $a x + b y + c = 0$ will always pass through a fixed point whose coordinates are .........

The orthocentre of the triangle formed by the lines $x + y = 1, 2 x + 3 y = 6$ and $4 x - y + 4 = 0$ lies in quadrant number .........