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Consider the family of circles x^(2)+y^(...

Consider the family of circles `x^(2)+y^(2)-2x-6y-8=0` passing through two fixed points A and B . Also, `S=0` is a cricle of this family, the tangent to which at A and B intersect on the line `x+2y+5=0`.
If the circle `x^(2)+y^(2)-10x+2y+c=0` is orthogonal to `S=0`, then the value of c is

A

8

B

9

C

10

D

12

Text Solution

Verified by Experts

The correct Answer is:
4
Circle `x^(2)+y^(2)-10x+2y+c=0` is orthogonal to `x^(2)+y^(2)-2x-6y-8=0`.
So, by applying condition of orthogonal intersection, we get
`2(-5)(-1)+2(1) (-3)= c-8`
`:. C= 12`
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CENGAGE-CIRCLE -Exercise (Comprehension)
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  2. Give two circles intersecting orthogonally having the length of common...

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  3. Give two circles intersecting orthogonally having the length of common...

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  4. Give two circles intersecting orthogonally having the length of common...

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  5. In the given figure, there are two circles with centers A and B. The c...

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  6. In the given figure, there are two circles with centers A and B. The c...

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  7. In the given figure, there are two circles with centers A and B. The c...

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  8. Let each of the circles S(1)-=x^(2)+y^(2)+4y-1=0 S(1)-= x^(2)+y^(2...

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  9. Let each of the circles S(1)-=x^(2)+y^(2)+4y-1=0 S(1)-= x^(2)+y^(2...

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  10. Let each of the circles S(1)-=x^(2)+y^(2)+4y-1=0 S(1)-= x^(2)+y^(2...

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  11. The line x + 2y = a intersects the circle x^2 + y^2 = 4 at two distinc...

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  12. The line x + 2y = a intersects the circle x^2 + y^2 = 4 at two distinc...

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  13. Let A,B, and C be three sets such that A={(x,y)|(x)/(cos theta)=(y)/...

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  14. Let A,B, and C be three sets such that A={(x,y)|(x)/(cos theta)=(y)/...

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  15. Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through...

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  16. Show that equation x^2+y^2-2ay-8=0 represents, for different values o...

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  17. Consider the family of circles x^(2)+y^(2)-2x-6y-8=0 passing through ...

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  18. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  19. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  20. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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