Equation of a circle in standard form, Equations of tangent and normal at a point P on a given circle, Condition for the line y = mx + c to be a tangent to the circle and finding the point of contact - Maths Book back answers and solution for Exercise questions

EXERCISE 5.1

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.

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

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

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

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

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

8. If *y *= 2√2*x *+ *c *is a tangent to the circle *x*2 + *y*2 = 16 , find the value of *c *.

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

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

11. Find centre and radius of the following circles.

(i) *x*2 + ( *y *+ 2)2 = 0

(ii) *x*2 + *y*2 + 6*x *- 4 *y *+ 4 = 0

(iii) *x*2 + *y*2 - *x *+ 2 *y *- 3 = 0

(iv) 2*x*2 + 2 *y*2 − 6*x** *+ 4 *y *+ 2 = 0

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

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12th Mathematics : UNIT 5 : Two Dimensional Analytical Geometry II : Exercise 5.1: Circle | Problem Questions with Answer, Solution

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