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

MCQ

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

A
a pair of straight lines
B
an ellipse
✓
a hyperbola
D
a parabola

✓

Answer

Correct option: C.

a hyperbola

(C)
$\begin{array}{l}x^2-2 x-4 y^2+16 y-40=0 \\ \Rightarrow\left(x^2-2 x\right)-4\left(y^2-4 y\right)-40=0 \\ \Rightarrow(x-1)^2-1-4\left[(y-2)^2-4\right]-40=0 \\ \Rightarrow(x-1)^2-4(y-2)^2=25 \\ \Rightarrow \frac{(x-1)^2}{25}-\frac{(y-2)^2}{\frac{25}{4}}=1, \text { which is a hyperbola. }\end{array}$

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