Question

The latus rectum of the conic 3x² + 4y² – 6x + 8y – 5 = 0 is :

• A. 3
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{2}{\sqrt{3}}$
• D. None of these

Answer 1

Answer: (A)

3

Answer 2

Given conic is

3(x– 1)² + 4(y + 1)² = 12

Ž $\frac{(x - 1)^{2}}{4}$ + $\frac{(y + 1)^{2}}{3}$ = 1

Ž $\frac{X^{2}}{4}$ + $\frac{Y^{2}}{3}$ = 1 {X= x – 1, Y = y + 1}

which is an ellipse

here a² = 4 b² = 3

latus rectum = 2. $\frac{b^{2}}{a}$ = 2. $\frac{3}{2}$ = 3