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Prove that the tangent to the circle x^2...

Prove that the tangent to the circle `x^2 + y^2 - 8x + 6y + 20 = 0` and find its point of contact.`

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PATHFINDER-CIRCLE-QUESTION BANK
  1. Find the equations of the tangents drawn from the point A(3, 2) to the...

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  2. Find the value of alpha for which the point (alpha, alpha + 2) is an i...

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  3. Prove that the tangent to the circle x^2 + y^2 - 8x + 6y + 20 = 0 and ...

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  4. Find the equation of the circle which passes through (1, 1) and cuts o...

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  5. A variable circle passes through the point A(a, b) and touches the x-a...

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  6. If the two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 cut the co-...

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  7. The locus of the centre of the circle of radius 2 which rolls on the i...

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  8. Four distinct points (2k,3k),(1,0),(0,1)and(0,0) lie on a circle for

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  9. The circle described on the line joining the points (0,1),(a,b) as dia...

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  10. The centre of a circle passing through the points (0,0),(1,0)and touch...

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  11. One of the diameter of the circle x^2+y^2-12x+4y+6=0 is given by

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  12. The coordinates of middle point of the chord 2x-5y+18=0 cut of by the ...

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  13. If a circle passes through the point intersection of the co-ordinate a...

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  14. The co-ordinates of the point on the circle x^2+y^2-12x+30=0 which is ...

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  15. If (2,5) is an interior point of the circle x^2+y^2-8x-12y+P=0 and the...

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  16. The range of values of r for which the point (-5+r/sqrt2,-3+r/sqrt2) i...

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  17. P is a point(a,b) in the first quadrant. If the two circles which pass...

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  18. The circles having radii r1 and r2 intersect orthogonally. Length of t...

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  19. The straight line y=mx+c cuts the circle x^2+y^2=a^2 at real points if

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  20. A line is drawn through a fixed point P(alpha,beta)to cut the circle x...

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