Question

The equation of the ellipse whose centre is (2,3), vertex is (5,3) the length of major axis is 6 and minor axis is 4 is

• A. $\frac{(x - 2)^{2}}{9}\mspace{6mu} + \mspace{6mu}\frac{(y - 3)^{2}}{4}$ = 1
• B. $\frac{(x - 2)^{2}}{4}\mspace{6mu} + \mspace{6mu}\frac{(y - 3)^{2}}{9}$ = 1
• C. $\frac{(x + 2)^{2}}{9}\mspace{6mu} + \mspace{6mu}\frac{(y + 3)^{2}}{4}$ = 1
• D. $\frac{(x + 2)^{2}}{4}\mspace{6mu} + \mspace{6mu}\frac{(y + 3)^{2}}{9}$ = 1

Answer 1

Answer: (A)

$\frac{(x - 2)^{2}}{9}\mspace{6mu} + \mspace{6mu}\frac{(y - 3)^{2}}{4}$ = 1

Answer 2

Since centre = (2, 3) = (α, β), vertex = (5, 3) the major axis is parallel to x-axis.

Given 2a = 6 ⇒ a = 3

2b = 4 ⇒ b = 2

∴ The equation of ellipse is $\frac{(x - \alpha)^{2}}{a^{2}} + \frac{(y - \beta)^{2}}{b^{2}} = 1$

$\frac{(x - 2)^{2}}{9} + \frac{(y - 3)^{2}}{4} = 1$