WBJEE · Maths · Hyperbola
Let \(16 x^{2}-3 y^{2}-32 x-12 y=44\) represents a hyperbola. Then,
- A length of the transverse axis is \(2 \sqrt{3}\)
- B length of each latusrecturn is \(32 / \sqrt{3}\)
- C eccentricity is \(\sqrt{19 / 3}\)
- D equation of a directrix is \(x=\frac{\sqrt{19}}{3}\)
Answer & Solution
Correct Answer
(C) eccentricity is \(\sqrt{19 / 3}\)
Step-by-step Solution
Detailed explanation
Given equation of hyperbola is \(16 x^{2}-3 y^{2}-32 x-12 y=44\) \(\Rightarrow 16 x^{2}+16-32 x-3 y^{2}-12-12 y\) \(=44+4\) \(\Rightarrow 16(x-1)^{2}-3(y+2)^{2}=48\) \(\Rightarrow \quad \frac{(x-1)^{2}}{3}-\frac{(y+2)^{2}}{16}=1\) On comparing the equation with standard equation…
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