Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the line, y = m x + 5 m m ≠ 0 is their common tangent, then m satisfi

Question

Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the line, y = m x + 5 m m &#8800; 0 is their common tangent, then m satisfies m 4 - 3 m 2 + 2 = 0 .

Quantrex Academy · Accepted Answer

Correct answer: D. Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for statement - I .

Tangent to y 2 = 4 5 x will be y = m x + 5 m As tangent to x 2 + y 2 = 5 2 will be y = m x &#177; 5 2 1 + m 2 Hence for common tangent 5 m = 5 2 1 + m 2 &#8658; m 4 + m 2 - 2 = 0 &#8658; m 2 = 1 , m 2 = &#8722; 2 (Not Possible) &#8658; m = &#177; 1 Hence common tangent is y = x + 5 Both the statements are correct The values of m also satisfy the equation in statement - II but it is not a correct explanation for statement - I .

Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the line, y = m x + 5 m m ≠ 0 is their common tangent, then m satisfies m 4 - 3 m 2 + 2 = 0 .

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More from Circle

Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the line, y = m x + 5 m m &#8800; 0 is their common tangent, then m satisfies m 4 - 3 m 2 + 2 = 0 .

Options

Correct answer

Step-by-step solution

More from Circle

Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the line, y = m x + 5 m m ≠ 0 is their common tangent, then m satisfies m 4 - 3 m 2 + 2 = 0 .