JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q76

MathematicsSingle correct+4 / -1Question 76 of 90

Let the curves $y^2=kx$ and $xy=-1$ have a common tangent, whose slope is $\dfrac12$ . Then k can NOT lie in the interval

(2, 4]

(−3, −1)

[−4, −3)

(1, 3)

Answer and worked solution

Official answer: C

Tangent to xy = −1 with slope ½: $y=\frac x2+c$ gives $\frac{x^2}2+cx+1=0$ with a double root, $c=\pm\sqrt2$ .

Parabola tangent $y=mx+\frac k{4m}$ : $\frac k2=\pm\sqrt2$ , $k=\pm2\sqrt2\approx\pm2.83$ . Both values miss $[-4,-3)$ only.

(C)

Topics:Tangents and normals to conics Parabola

JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 76