Let the circle $x^2 + y^2 = 2ax + 2by$ intersect the x-axis at point $A(\alpha, 0)$ and y-axis at point $B(0, \beta)$, where $\alpha\beta \neq 0$. If the point $C(p, q)$ lies on the chord…

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Let the circle $x^2 + y^2 = 2ax + 2by$ intersect the x-axis at point $A(\alpha, 0)$ and y-axis at point $B(0, \beta)$, where $\alpha\beta \neq 0$. If the point $C(p, q)$ lies on the chord AB, then $\frac{p+\alpha}{a} + \frac{q+\beta}{b}$ equals

Accepted Answer

C - 6. Circle meets the axes at A(2a,0) and B(0,2b), so alpha = 2a, beta = 2b. C on AB: p/(2a) + q/(2b) = 1, i.e. p/a + q/b = 2. Expression = p/a + q/b + alpha/a + beta/b = 2 + 2 + 2 = 6.

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A - 4

Answer

B - 2

Answer

D - 3

Let the circle \(x^2 + y^2 = 2ax + 2by\) intersect the x-axis at point \(A(\alpha, 0)\) and y-axis at point \(B(0, \beta)\), where \(\alpha\beta \neq 0\). If the point \(C(p, q)\) lies on the chord…

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