Q.
The locus of the midpoints of the chord of the circle, x2+y2=25 which is tangent to the hyperbola, x29-y216=1 is
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a
x2+y22−16x2+9y2=0
b
x2+y22−9x2−16y2=0
c
x2+y22−9x2+144y2=0
d
x2+y22−9x2+16y2=0
answer is D.
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Detailed Solution
Equation of the chord having mid point h,k to the circle x2+y2=25 is hx+ky=h2+k2it can be written as y=−hkx+h2+k2kGiven this is tangent to the hyperbola x29−y216=1c2=a2m2-b2⇒h2+k2k2=9h2k2−16⇒h2+k22=9h2−16k2The locus is x2+y22=9x2-16y2 or x2+y22-9x2+16y2=0
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