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The equation x^(2)+y^(2)-6x+8y+25=0 repr...

The equation `x^(2)+y^(2)-6x+8y+25=0` represents

A

a point (3, -4)

B

a pair of straight lines x=3, y=-4

C

a circle of non-zero radius

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`x^(2)+y^(2)-6x+8y+25=0`
`rArr (x-3)^(2)+(y+4)^(2)=0`
`rArr x-3=0` and `y+4=0`
`rArr x=3, y=-4`, which gives the point (3, -4).
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OBJECTIVE RD SHARMA-CIRCLES-Section I - Solved Mcqs
  1. The equation x^(2)+y^(2)-6x+8y+25=0 represents

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  2. The number of integral values of lambda for which the equation x^(2)+y...

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  3. If the equation x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0 represen...

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  4. If 2(x^(2)+y^(2))+4 lambda x + lambda^(2)=0 represents a circle of mea...

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  5. The locus of a point which moves such that the sum of the square of it...

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  6. Prove that the locus of a point which moves such that the sum of th...

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  7. The equation of the circle passing through the point (-1, 2) and havi...

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  8. A circle of radius 'r' passes through the origin O and cuts the axes a...

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  9. The equation (x^2 - a^2)^2 + (y^2 - b^2)^2 = 0 represents points

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  10. Find the greatest distance of the point P(10 ,7) from the circle x^2+y...

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  11. If the base of a triangle and the ratio of the lengths of the other tw...

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  12. Two conics a1x^2+2h1xy + b1y^2 = c1, a2x^2 + 2h2xy+b2y^2 = c2 interse...

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  13. The number of points with integral coordinates that are interior to t...

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  14. Find the equation of the circle which is touched by y=x , has its cent...

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  15. The locus of the centre of the circle which cuts the circle x^2 + y^2 ...

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  16. From the point A(0,3) on the circle x^2 +4x + (y-3)^2 = 0 a chord AB ...

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  17. Two vertices of an equilateral triangle are (-1,0) and (1, 0), and its...

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  18. The geometric mean of the minimum and maximum values of the distance...

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  19. A circle passes through a fixed point A and cuts two perpendicular str...

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  20. The equation of the circumcircle of the triangle formed by the lines w...

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