JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The tangents to the curve \(y = (x -2)^2 -1\) at its points of intersection with the line \(x -y = 3\), intersect at the point
- A \(\left( {\frac{5}{3},1} \right)\)
- B \(\left( {-\frac{5}{2},-1} \right)\)
- C \(\left( {-\frac{5}{2},1} \right)\)
- D \(\left( {\frac{5}{2},-1} \right)\)
Answer & Solution
Correct Answer
(D) \(\left( {\frac{5}{2},-1} \right)\)
Step-by-step Solution
Detailed explanation
\(x - y - 3 = 0\,\,\,\,\,\,\,\,\,\,......\left( i \right)\) will be chord of contact of parabola Let the required point is \(P\left( {{x_1},{y_1}} \right)\) chord of contact for point \(P\) is \(\frac{{y + {y_1}}}{2} = x{x_1} - 4\frac{{\left( {x + {x_1}} \right)}}{2} + 3\)…
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