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Conic Section

Short Answer Type

1. In each of the following, find the equation of circle with centre (-2, 3) and radius 4

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2. In each of the following, find the equation of circle with centre

open parentheses 1 half comma space 1 fourth close parentheses

and radius

1 over 12

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3. In each of the following, find the equation of circle with centre (-a, -b) and radius

space space space space square root of straight a squared minus straight b squared end root

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4. Find the equation of a circle with centre at (2, 2) and passes through the point (4,5).

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Long Answer Type

5. Find the equation of a circle which pass through the points O (0, 0), A (4, 0) and B (0, 3).

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6. Find the equation of the circle passes through (0, 0) and making intercepts a and b on the co-ordinate axes.

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Short Answer Type

7. Find the equation of a circle whose centre is (3, –2) and has an area of 154 square units.

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8. Find the equation of a circle having radius 5 units and the centre as the point of intersection of the straight lines 2x – y – 5 = 0 and 3x + 2y = 4.

Radius, r of the circle = 5 ...(i)
The centre is the point of intersection of straight lines
2x - y - 5=0 and 3x + 2y = 4
Solving these two equations simultaneously, we have
4x - 2y = 10
3x + 2y = 4
Adding, we get 7x = 14 or x = 2
$rightwards double arrow$ 4 - y - 5 = 0 or y = -1
∴ The co-ordinates of the centre are (2, -1)
$rightwards double arrow$ h = 2, k = -1 and r = 5
The equation of the circle in the standard form is:
$left parenthesis straight x minus straight h right parenthesis squared plus left parenthesis straight y minus straight k right parenthesis squared equals straight r squared space space space space space space space or space space left parenthesis straight x minus 2 right parenthesis space plus space left parenthesis straight y plus 1 right parenthesis squared space equals space left parenthesis 5 right parenthesis squared$
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which is the required equation of the circle.

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9. Find the equation of a circle, two of whose diameters are along the straight lines x – 2y = 7 and x + 2y + 1 = 0 and which passes through the point (1, 4).

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10. Find the equation of a circle having centre at point C(–2, 3) and touching the straight line 3x – 4y – 2 = 0.

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