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

If the distance between the parallel lines given by the equation $x^2+4xy+4y^2+3x+6y-4=0$ is $\lambda$,then $\lambda^2=$

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The lines joining the points of intersection of the curve $5x^2 + 12xy - 8y^2 + 8x - 4y + 12 = 0$ and the line $x - y = 2$ to the origin make angles with the axes that are:

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The acute angle between the pair of straight lines joining the origin to the points of intersection of the line $x+y-1=0$ with the pair of straight lines $k x^2+8 x y-3 y^2+2 x-4 y-1=0$ is

DifficultTS EAMCET 2020

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The distance between the pair of parallel lines represented by $x^2+2xy+y^2-8ax-8ay-9a^2=0$ is $...$ units.

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The pair of lines joining the origin to the points of intersection of the line $x-y=2$ with the curve $5x^2+12xy-8y^2+8x-4y+12=0$ are equally inclined to 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

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If the distance between the parallel lines given by the equation $x^2+4xy+4y^2+3x+6y-4=0$ is $\lambda$,then $\lambda^2=$

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