WBJEE · Maths · Parabola
The line \(y=x+5\) touches
- A the parabola \(y^2=20 x\)
- B the ellipse \(9 x^2+16 y^2=144\)
- C the hyperbola \(\frac{x^2}{29}-\frac{y^2}{4}=1\)
- D the circle \(x^2+y^2=25\)
Answer & Solution
Correct Answer
(C) the hyperbola \(\frac{x^2}{29}-\frac{y^2}{4}=1\)
Step-by-step Solution
Detailed explanation
(A) \(y^2=20 x=4(5) x \quad \therefore\) Tangent \(: y=m x+\frac{a}{m}\) for \(m=1, a=5\) \(\therefore \mathrm{y}=\mathrm{x}+5\) is a tangent to \(\mathrm{y}^2=20 \mathrm{x}\) (B) \(9 x^2+16 y^2=144\) \(c^2=a^2 m^2+b^2 \quad y=x+5 \Rightarrow m=1 ; c=5\)…
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