If $(1,\ a),\ (b,\ 2)$ are conjugate points with respect to the circle $x^{2} + y^{2} = 25$, then $4a + 2b$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
Equation of circle is
$x^{2} + y^{2} = 25$ ..(i)
Polar equation of a circle with respect to the point $(1,\ a)$ and $(b,\ 2)$ is
$x + ay = 25$ …(ii)
and $bx + 2y = 25$ …(iii)
since, $(1,\ a)$ and $(b,\ 2)$ are the conjugate point of a circle, therefore point $(1,\ a)$ satisfy the Eq. (iii), we get
$b + 2a = 25\  \Rightarrow \ 2b + 4a = 50$

Q. If $(1,\ a),\ (b,\ 2)$ are conjugate points with respect to the circle $x^{2} + y^{2} = 25$, then $4a + 2b$ is equal to

Explanation

Reviewed by Dr. Abubacker

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