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Maths-

General

Easy

Question

The circle $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 lambda x equals 0 comma lambda element of R$ touches the parabola y² = 4x externally. Then

$λ$ $>$ 0
$λ$ $<$ 0
$λ$ $>$ 1
none of these

hint Hint:

Identify the center and radius of circle .To touch externally the center of circle should lie out side of parabola. Then S > 0 at the center of circle.

The correct answer is: $lambda$ $greater than$ 0

The circle $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 lambda x equals 0 comma lambda element of R$ touches the parabola y² = 4x externally.
$x squared plus y squared space plus 2 lambda x space equals space 0 space rightwards double arrow x squared space plus 2 lambda x space plus space lambda squared space plus y squared equals space space lambda squared rightwards double arrow open parentheses x plus lambda close parentheses squared space plus left parenthesis y minus 0 right parenthesis squared space equals space space lambda squared$
The radius of circle is (- $lambda$ ,0) and radius is $open vertical bar lambda close vertical bar$ .
To touch externally the center of circle should lie out side of parabola.
Then y²- 4x > 0 at (- $lambda$ ,0)
0 - 4(- $lambda$ ) > 0 then 4 $lambda$ >0
Therefore, $lambda$ > 0 is the condition to The circle touches the parabola externally.

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