First slide

Definition of a circle

Question

The coordinates of the centre and radius of the circle represented by the equation
$(3 - 2 λ) x^{2} + λ y^{2} - 4 x + 2 y - 4 = 0$ are

Moderate

A

(2, 1), 3
B

(- 2, 1), 3
C

(2, -1), 3
D

(2, -1), 1

Solution

The equation $(3 - 2 λ) x^{2} + λ y^{2} - 4 x + 2 y - 4 = 0$
will represent a circle if
$3 - 2 λ = λ \Rightarrow λ = 1$ $∵ Coeff. of x^{2} = Coeff. of y^{2}]$
Putting $λ = 1$ in the given equation, we get
The coordinates of centre and radius of the circle represented
by this equation are (2, -1) and 3 respectively.

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