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Find the parametric equation of the circ...

Find the parametric equation of the circles :
(i) `2x^(2) + 2y^(2) - 5x - 7y - 3 = 0 `
(ii) `3x^(2) + 3y^(2) + 4x - 6y - 4 = 0 `.

Text Solution

Verified by Experts

The correct Answer is:
`x = (5)/(4) + (7)/(4) sqrt(2) cos alpha, y = (7)/(4) + (7)/(4) sqrt(2) sin alpha`
(ii) = `(-2)/(3) + (5)/(4) cos alpha , y = 1 + (5)/(3) sin alpha`.
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(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

(i) x^(2) - 4x + 3 = 0 (ii) y^(2) - 7y+10 = 0