First slide

Cartesian plane

Question

lf points $(a^{2}, 0), (0, b^{2})$ and $(1, 1)$ are collinear, then

Easy

A

$\frac{1}{a^{2}} + \frac{1}{b^{2}} = 1$
B

$\frac{1}{a} + \frac{1}{b} = 1$
C

$a^{2} + b^{2} = 1$
D

none of these

Solution

Given points are collinear
$\begin{array}{l} ∴ |\begin{array}{ccc} a^{2} & 0 & 1 \\ 0 & b^{2} & 1 \\ 1 & 1 & 1 \end{array}| = 0 \\ \Rightarrow a^{2} (b^{2} - 1) + (0 - b^{2}) = 0 \Rightarrow a^{2} b^{2} = a^{2} + b^{2} \Rightarrow \frac{1}{a^{2}} + \frac{1}{b^{2}} = 1 \end{array}$

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