(C) The equation of the line is $y - 2\sqrt{2}x = c$,which can be written as $\frac{y - 2\sqrt{2}x}{c} = 1$.Homogenizing the circle $x^2 + y^2 = 2$ us

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(C) The equation of the line is $y - 2\sqrt{2}x = c$,which can be written as $\frac{y - 2\sqrt{2}x}{c} = 1$.Homogenizing the circle $x^2 + y^2 = 2$ using the line equation,we get:$x^2 + y^2 = 2 \left( \frac{y - 2\sqrt{2}x}{c} \right)^2$$c^2(x^2 + y^2) = 2(y^2 + 8x^2 - 4\sqrt{2}xy)$$c^2x^2 + c^2y^2 = 2y^2 + 16x^2 - 8\sqrt{2}xy$$(c^2 - 16)x^2 + 8\sqrt{2}xy + (c^2 - 2)y^2 = 0$Since the lines are at right angles,the sum of the coefficients of $x^2$ and $y^2$ must be zero:$(c^2 - 16) + (c^2 - 2) = 0$$2c^2 - 18 = 0$$c^2 = 9$$c^2 - 9 = 0$.

Class 11 Mathematics Pair of straight lines Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

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The pair of straight lines joining the origin to the points of intersection of the line $y = 2\sqrt{2}x + c$ and the circle $x^2 + y^2 = 2$ are at right angles,if

A
$c^2 - 4 = 0$
B
$c^2 - 8 = 0$
C
$c^2 - 9 = 0$
D
$c^2 - 10 = 0$

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Pair of straight lines

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Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

Find the equation of the pair of lines joining the origin to the points of intersection of the circle $x^2 + y^2 = 4$ and the line $2x + 3y - 4 = 0$.

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The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $x^2+y^2+xy+x+3y+1=0$ and the line $x+y+2=0$ is

MediumAP EAMCET 2024

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The equation of the pair of lines joining the origin to the points of intersection of two circles $x^2+y^2-4x+8y+5=0$ and $x^2+y^2+2x+4y-3=0$ is

MediumAP EAMCET 2018

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The straight lines joining the origin to the points of intersection of the line $2x + y = 1$ and the curve $3x^2 + 4xy - 4x + 1 = 0$ include an angle of:

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If the angle between the lines joining the origin to the points of intersection of $x+2y+\lambda=0$ and $2x^2-2xy+3y^2+2x-y-1=0$ is $\frac{\pi}{2}$,then a value of $\lambda$ is

MediumAP EAMCET 2025

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The pair of straight lines joining the origin to the points of intersection of the line $y = 2\sqrt{2}x + c$ and the circle $x^2 + y^2 = 2$ are at right angles,if

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Find the equation of the pair of lines joining the origin to the points of intersection of the circle $x^2 + y^2 = 4$ and the line $2x + 3y - 4 = 0$.

The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $x^2+y^2+xy+x+3y+1=0$ and the line $x+y+2=0$ is

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