First slide

Definition of a circle

Question

Equation of the circle which touches $3 x + 4 y = 7$ and passes through $(1, - 2)$ and $(4, - 3)$ , is

Moderate

A

$x^{2} + y^{2} - 94 x + 18 y + 55 = 0$
B

$15 x^{2} + 15 y^{2} - 94 x + 18 y + 55 = 0$
C

$15 x^{2} + 15 y^{2} + 94 x + 18 y + 55 = 0$
D

$x^{2} + y^{2} - 94 x - 18 y + 55 = 0$

Solution

Clearly, circle $15 x^{2} + 15 y^{2}$ $- 94 x + 18 y + 55 = 0$ passes through $(1, - 2)$ and $(4, - 3)$ . Also, it touches $3 x + 4 y = 7$ .

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