PRACTICE QUESTIONS ON FINDING EQUATION OF CIRCLE FOR GRADE 12

(1)  Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

Solution

(2)  Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.  Solution

(3)  Find the equation of circles that touch both the axes and pass through (-4,-2) in general for.     Solution

(4)  Find the equation of the circle with centre (2,3) and passing through the intersection of the lines 3x − 2y −1 = 0 and 4x + y − 27 = 0        Solution

(5)  Obtain the equation of the circle for which (3, 4) and (2,-7) are the ends of a diameter.            Solution

(6)  Find the equation of the circle through the points (1, 0), (-1, 0) and (0, 1) .         Solution

(7) A circle of area 9π  square units has two of its diameters along the lines x + y = 5 and x − y = 1. Find the equation of the circle.         Solution

(8)  If y = 2√2x + c is a tangent to the circle x² + y² = 16 , find the value of c        Solution

(9)  Find the equation of the tangent and normal to the circle x²+ y² − 6x + 6y − 8 = 0 at (2, 2) .        Solution

(10)  Determine whether the points (-2, 1),(0, 0) and (-4, -3) lie outside, on or inside the circle x² + y² − 5x + 2y − 5 = 0 .        Solution

(11)  Find centre and radius of the following circles.

(i) x² + (y + 2)² = 0

(ii)  x² + y² + 6x − 4y + 4 = 0

(iii) x² + y² − x + 2y − 3 = 0

(iv) 2x² + 2y² − 6x + 4y + 2 = 0        Solution

(12)  If the equation 3x² + (3 − p) xy + qy² − 2 px = 8pq represents a circle, find p and q . Also determine the centre and radius of the circle.          Solution

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