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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.

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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.

Centre of the required circle is C (-2, 3)
Let line AB with equation 3x - 4y - 2 = 0 touches the circle at point L
∴ p = r
where p, is length of perpendicular CL and r is the radius
$rightwards double arrow$ $open vertical bar fraction numerator 3 left parenthesis negative 2 right parenthesis minus 4 left parenthesis 3 right parenthesis minus 2 over denominator square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root end fraction close vertical bar space equals space straight r space space space space rightwards double arrow space space straight r equals open vertical bar fraction numerator negative 20 over denominator 5 end fraction close vertical bar space equals space 4$
The equation of circle is:
$left parenthesis straight x minus straight h right parenthesis squared plus left parenthesis straight y minus straight k right parenthesis squared space equals space straight r squared space or space left parenthesis straight x plus 2 right parenthesis squared space plus space left parenthesis straight y minus 3 right parenthesis squared space equals space left parenthesis 4 right parenthesis squared$
or $space space straight x squared plus straight y squared plus 4 straight x minus 6 straight y minus 3 equals 0$
Hence, the equation of circle is: $space space straight x squared plus straight y squared plus 4 straight x minus 6 straight y minus 3 equals 0$

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