Practice Questions on Finding Equation of Circle for Grade 12 :
Here we are going to see some practice questions on finding equation of circle.
(1) Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.
(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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