The families of curves defined by the equations $y = a x, y^{2} + x^{2} = c^{2}$ are perpendicular for

= 2,

= 4

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= - 2,

= 3

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= 3,

= 2

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= 3,

= - 2

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Solution

The correct options are
A a $= 2,$ c $= 4$
B a $= 3,$ c $= 2$
C a $= - 2,$ c $= 3$
D a $= 3,$ c $= - 2$
Since, the straight line $y = a x$ passes through the center of the circle $x^{2} + y^{2} = c^{2}$
Therefore, $y = a x$ is normal to circle $x^{2} + y^{2} = c^{2}$ always for all values of $a$ & $c$
Ans: A,B,C,D

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Similar questions

If two of the three lines represented by the equation $a x^{3} + b x^{2} y + c x y^{2} + d y^{3} = 0$ are perpendicular, then

a) y = x^{2}, b) y = 4 x^{2} & c) y = 8 x^{2}

a x + b y + c z = k

a^{2} x + b^{2} y + c^{2} z = k^{2}

a^{3} x + b^{3} y + c^{3} z = k^{3}

c (y + c)^{2} + x^{3}

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