If the parabola y - x 2-2 x - k touches the parabola y -1-2 x 2-4 x -3- then the value of k isA- 2B- 1C- 3D- 4

The correct option is B 1If the parabolas intersect each other, then x^2 2x+k= 12x^2 4x+3 ⇒ x^2 4x+2(3 k)=0⋯(1) For the given parabolas to touch at one point, ...

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Standard XII

Mathematics

Focii of Hyperbola

If the parabo...

Question

If the parabola $y = - x^{2} - 2 x + k$ touches the parabola $y = - \frac{1}{2} x^{2} - 4 x + 3$ , then the value of $k$ is

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Solution

The correct option is A $1$
If the parabolas intersect each other, then
$- x^{2} - 2 x + k = - \frac{1}{2} x^{2} - 4 x + 3 \Rightarrow x^{2} - 4 x + 2 (3 - k) = 0 \dots (1)$
For the given parabolas to touch at one point,
$D = 0 \Rightarrow (- 4)^{2} - 4 \times 2 \times (3 - k) = 0 \Rightarrow 8 k - 8 = 0 \Rightarrow k = 1$

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If the parabola y=−x2−2x+k touches the parabola y=−12x2−4x+3, then the value of k is

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If the parabola $y = - x^{2} - 2 x + k$ touches the parabola $y = - \frac{1}{2} x^{2} - 4 x + 3$ , then the value of $k$ is