Questions
The locus of the centre of a circle which cuts orthogonally the circle and which touches
is
a
y2=16x+4
b
x2=16y
c
x2=16y+4
d
y2=16x
detailed solution
Correct option is D
Let the circle be x2+y2+2gx+2fy+c=0It cuts the circle x2+y2−20x+4=0 orthogonally∴ 2(−10g+0×f)=c+4⇒ −20g=c+4Circle (i) touches the line x = 2 i.e. x + Oy - 2 = 0∴ −g+0−212+02=g2+f2−c⇒ (g+2)2=g2+f2−c⇒4g+4=f2−cEliminating c from (ii) and (iii), we get−16g+4=f2+4⇒f2+16g=0Hence, the locus of (−g,−f) is y2−16x=0Talk to our academic expert!
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