JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The tangent to the parabola \(y^2 = 4x\) at the point where it intersects the circle \(x^2 + y^2 = 5\) in the first quadrant, passes through the point
- A \(\left( { - \frac{1}{3},\frac{4}{3}} \right)\)
- B \(\left( {\frac{3}{4},\frac{7}{4}} \right)\)
- C \(\left( { - \frac{1}{4},\frac{1}{2}} \right)\)
- D \(\left( {\frac{1}{4},\frac{3}{4}} \right)\)
Answer & Solution
Correct Answer
(B) \(\left( {\frac{3}{4},\frac{7}{4}} \right)\)
Step-by-step Solution
Detailed explanation
\({x^2} + 4x = 5\) \( \Rightarrow x = - 5,x = 1\) \( \Rightarrow P\left( {1,2} \right)\) Tangent at \(P\) is \(y = x + 1\) \(\left( {\frac{3}{4},\frac{7}{4}} \right)\) lies on this.
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