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Maths-

General

Easy

Question

If the line $x plus y plus k equals 0$ is a tangent to the parabola $x to the power of 2 end exponent equals 4 y$ then k=

1
2
3
4

Hint:

The parabola equation is simplest if the vertex is at the origin and the axis of symmetry is along the x-axis and y-axis.
$x squared space equals space 4 a y$
In parabola a line to be a tangent to parabola, condition is $c space equals space a over m$

The correct answer is: 1

Given Parabola : $x to the power of 2 end exponent equals 4 y$
Comparing with standard equation of parabola $x squared space equals space 4 a y$
4ay = 4y
a = 1
Given line : $x plus y plus k equals 0$
Comparing with standard equation of line $y space equals space m x space plus space c$

m = 1 and c = k
In parabola a line to be a tangent to parabola, condition is $c space equals space a over m$
Substituting these values
$k space equals space 1 over 1$
Thus, If the line $x plus y plus k equals 0$ is a tangent to the parabola $x to the power of 2 end exponent equals 4 y$ then k= 1

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