x^2 - 4 y^2 - 2x + 16y - 40 = 0 represents - Vidyadip

MCQ

${x^2} - 4{y^2} - 2x + 16y - 40 = 0$ represents

A
A pair of straight lines
B
An ellipse
✓
A hyperbola
D
A parabola

✓

Answer

Correct option: C.

A hyperbola

c
(c) ${x^2} - 2x - 4{y^2} + 16y - 40 = 0$

==> $({x^2} - 2x) - 4({y^2} - 4y) - 40 = 0$

==> ${(x - 1)^2} - 1 - 4[{(y - 2)^2} - 4] - 40 = 0$

==> ${(x - 1)^2} - 4{(y - 2)^2} = 25$

==> $\frac{{{{(x - 1)}^2}}}{{25}} - \frac{{{{(y - 2)}^2}}}{{25/4}} = 1$, which is a hyperbola.

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