First slide

Ellipse

Question

$The equation 2 x^{2} + 3 y^{2} - 8 x - 18 y + 35 = k represents$

Moderate

A

$no locus if k > 0$
B

$an ellipse if k > 0$
C

$a point if k = 0$
D

$a hyperbola if k > 0$

Solution

We have
$\begin{array}{l} 2 x^{2} + 3 y^{2} - 8 x - 18 y + 35 = k \\ or 2 (2 x^{2} - 4 x) + 3 (y^{2} - 6 y) + 35 = k \\ or 2 (x - 2)^{2} + 3 (y - 3)^{2} = k \\ for k = 0, we get \\ 2 (x - 2)^{2} + 3 (y - 3)^{2} = 0 \end{array}$
which represents the point (2,3).

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App