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Show that the circles x^2+y^2-10 x+4y-20...

Show that the circles `x^2+y^2-10 x+4y-20=0` and `x^2+y^2+14 x-6y+22=0` touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

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Show that the circles x^(2)+y^(2)-10x+4y-20=0 and x^(2)+y^(2)+14x-6y+22=0 touch each other.Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Find the coordinates of the points at which the circles x^2+y^2-4x-2y=4 and x^2+y^2-12x-8y=12 touch each other. Find the coordinates of the point of contact and equation of the common tangent at the point of contact.

Show that the circles x ^(2) + y ^(2) - 2x =0 and x ^(2) + y ^(2) - 8x + 12=0 touch each other externally. Find the point of contact.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

If the circles x^2+y^2+2x-8y+8=0 and x^2+y^2+10x-2y+22=0 touch each other find their point of contact

Show that the two circles x^(2) + y^(2) - 4x + 10y + 20 = 0 and x^(2) + y^(2) + 8x - 6y - 24 =0 touch each other . Also , find co-ordinates of their point of contact .

Show that the two circles x^(2) + y^(2) + 4x - 12 y + 4 = 0 and x^(2) + y^(2) - 2x - 4y + 4 = 0 touch each other . Also , find the co-ordinates of the point of contact .

A DAS GUPTA-Circles-EXERCISE
  1. Determine all those values of p in R for which two chords can be drawn...

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  2. A circle of radius 2 lies in the first quadrant and touches both the a...

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  3. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  4. Two circles, each of radius 5 units, touch each other at (1, 2). If th...

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  5. Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touc...

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  6. The equation of the circle which touches the circle x^2+y^2-6x+6y+17 =...

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  7. Find the area of equilateral triangle inscribed in a circle x^2+y^2+2g...

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  8. Find the area of the triangle formed by the tangents from the point (4...

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  9. Find the equations of the circles passing through the point (-4,3) and...

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  10. The equation of one of the circles which touch the pair of lines x^2 -...

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  11. Lines 5x + 12 y -10=0 and 5x - 12y - 40=0touch a circle C(1) of diamet...

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  12. Find the equation of the circle passing through the points A(4,3). B(...

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  13. A circle touches both the x-axis and the line 4x-3y+4=0. Its centre is...

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  14. Obtain the equations of the straight lines passing through the point A...

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  15. The extremities of a diagonal of a rectangle are (-4,4) and (6,-1). A...

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  16. Tangents are drawn to the circle x^(2) + y^(2) = 12 at the points wher...

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  17. Find the equation of the tangent to the circle x^2 + y^2 - 80x - 60y +...

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  18. The tangent to the circle x^(2)+y^(2)=5 at the point (1, -2) also touc...

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  19. AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = A...

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  20. Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it...

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