If the circle C 1 = x 2 + y 2 = 16 intersects another circle C 2 of radius 5, in such a manner that the common chord is of maximum length and has a slope equal to 3 4 , then one of the co-ordinates of the centre of C 2 are

Question

If the circle $C_{1} = x^{2} + y^{2} = 16$ intersects another circle $C_{2}$ of radius 5, in such a manner that the common chord is of maximum length and has a slope equal to $\frac{3}{4}$ , then one of the co-ordinates of the centre of $C_{2}$ are

Smart Achievers · Accepted Answer

(2)

$Equation of common chord is y = \frac{3}{4} x \Rightarrow 3 x - 4 y = 0$

$Family of circle x^{2} + y^{2} - 4 + λ (3 x - 4 y) = 0$

$Equate radius of this circle as 5$

Solution

Q.
If the circle $C_{1} = x^{2} + y^{2} = 16$ intersects another circle $C_{2}$ of radius 5, in such a manner that the common chord is of maximum length and has a slope equal to $\frac{3}{4}$ , then one of the co-ordinates of the centre of $C_{2}$ are

1 $(\frac{9}{5}, \frac{12}{5})$

2 $(\frac{9}{5}, \frac{- 12}{5})$

3 $(\frac{12}{5}, \frac{9}{5})$

4 $(\frac{12}{5}, \frac{- 9}{5})$

Ans.
(2)

$Equation of common chord is y = \frac{3}{4} x \Rightarrow 3 x - 4 y = 0$

$Family of circle x^{2} + y^{2} - 4 + λ (3 x - 4 y) = 0$

$Equate radius of this circle as 5$

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Solution

Q. If the circle C1=x2+y2=16 intersects another circle C2 of radius 5, in such a manner that the common chord is of maximum length and has a slope equal to 34, then one of the co-ordinates of the centre of C2 are

1 (95,125)

2 (95,-125)

3 (125,95)

4 (125,-95)

Ans. (2) Equation of common chord is y=34x⇒3x-4y=0 Family of circle x2+y2-4+λ(3x-4y)=0 Equate radius of this circle as 5