CBSE Class 10 Maths (Basic) 2025 · Paper 430(B)/S · Question 36

Coordinate Geometry 4 marks Medium

A park is designed in the form of a circle with centre

O

. There is a fountain at the centre of the park and the entry gate is at point

A

on the boundary of the park. Let the coordinates of centre

O

(2 a - 1, 7)

and the coordinates of point

A

(- 3, - 1)

. Based on the above information, answer the following questions:

(i)If $a = 1$ , determine the radius of the circular park.[1]
(ii)If the centre of park is on $y$ -axis, then find the value of $a$ .[1]
(iii)(a)If the radius of the circular park is $10$ units, then find the possible values of $a$ .[2]
(iii)(b)If $B$ is another point on the boundary of the park such that $O B ⊥ O A$ , and the radius of the circular park is $10$ units, then determine the length of the chord $A B$ .[2]

Answer

(i) The radius is

45

units; (ii)

a = \frac{1}{2}

; (iii)(a)

a = 2

a = - 4

; OR (iii)(b)

A B = 102

units.

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