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If the chord of contact of the tangents drawn from the point `(h , k)` to the circle `x^2+y^2=a^2` subtends a right angle at the center, then prove that `h^2+k^2=2a^2dot`

A

`h^(2)+k^(2)=a^(2)`

B

`2(h^(2)+k^(2))=a^(2)`

C

`h^(2)-k^(2)=a^(2)`

D

`h^(2)+k^(2)=2a^(2)`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-CIRCLES-Exercise
  1. If the tangents are drawn to the circle x^2+y^2=12 at the point where ...

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  2. If the straight line x=2y+1=0 intersects the circle x^2+y^2=25 at poin...

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  3. If the chord of contact of the tangents drawn from the point (h , k) t...

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  4. Find the equation of the circle which cuts the three circles x^2+y^2-3...

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  5. The equation of a circle which passes through (2a, 0) and whose radica...

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  6. If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the cir...

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  7. If the pole of a straight line with respect to the circle x^(2)+y^(2)=...

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  8. Find the equation of the chord of the circle x^2+y^2=9 whose middle po...

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  9. Locus of the mid points of the chords of the circle x^2+y^2=a^2 which ...

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  10. If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2)...

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  11. Equation of circle symmetric to the circle x^(2)+y^(2)+16x -24y +183 =...

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  12. The number of the tangents that can be drawn from (1, 2) to x^(2)+y^(2...

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  13. Equation of the circle through the origin and making intercepts of 3 a...

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  14. If y=2x is a chord of the circle x^2+y^2-10 x=0 , find the equation of...

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  15. The tangent to x^(2)+y^(2)=9 which is parallel to y-axis and does not ...

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  16. The two circles x^(2)+y^(2)-5=0 and x^(2)+y^(2)-2x-4y-15=0

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  17. If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , th...

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  18. The circle x^(2)+y^(2)=4 cuts the circle x^(2)+y^(2)-2x-4=0 at the poi...

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  19. If the circle x^2+y^2+2gx+2fy+c=0 is touched by y=x at P such that O P...

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  20. The number of common tangents of the circles x^(2)+y^(2)+4x+1=0 and x...

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