First slide

Equation of line in Straight lines

Question

If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y² = 0 is

Moderate

A

$\frac{b}{a}$
B

$\frac{c}{a}$
C

$\frac{a}{c}$
D

$\frac{a}{b}$

Solution

Let a, b, c be in G.P. with common ratio r.
Then, b = ar and c = ar^2.
So, the equation of the line is ax + by + c = 0
⇒ ax + ary + ar² = 0 ⇒ x + ry + r² = 0
This line cuts the curve x + 2y² = 0
Eliminating x, we get 2y² – ry + r_² = 0
If the roots of the quadratic equation are y₁ and y₂, then
$y_{1} + y_{2} = \frac{r}{2} \Rightarrow 2 (y_{1} + y_{2}) = r = \frac{b}{a} = \frac{c}{b}$

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