Question

An ellipse has its centre at (1, –1) and semi-major axis = 8 and which passes through the point (1 3). Then the equation of the ellipse is-

• A. $\frac{(x + 1)^{2}}{64}$+$\frac{(y + 1)^{2}}{16}$ = 1
• B. $\frac{(x–1)^{2}}{64}$+$\frac{(y + 1)^{2}}{16}$ = 1
• C. $\frac{(x - 1)^{2}}{16}$+$\frac{(y + 1)^{2}}{16}$ = 1
• D. $\frac{(x + 1)^{2}}{64}$+$\frac{(y - 1)^{2}}{16}$ = 1

Answer 1

Answer: (B)

$\frac{(x–1)^{2}}{64}$+$\frac{(y + 1)^{2}}{16}$ = 1

Answer 2

Equation of the ellipse with centre at (1, –1) can be written as $\frac{(x - 1)^{2}}{a^{2}}$+$\frac{(y + 1)^{2}}{b^{2}}$= 1,

where a = semi-major axis and b = semi-minor axis.

If a = 8, then ellipse is $\frac{(x - 1)^{2}}{64}$+$\frac{(y + 1)^{2}}{b^{2}}$= 1.

This passes through (1, 3)

\ 0 + $\frac{16}{b^{2}}$ = 1 Ž b² = 16

Hence equation of ellipse is

$\frac{(x - 1)^{2}}{64}$+$\frac{(y + 1)^{2}}{16}$= 1.