If there exists at least one point on the circle `x^(2)+y^(2)=a^(2)` from which two perpendicular tangents can be drawn to parabola `y^(2)=2x`, then f

Question

If there exists at least one point on the circle `x^(2)+y^(2)=a^(2)` from which two perpendicular tangents can be drawn to parabola `y^(2)=2x`, then f

If there exists at least one point on the circle `x^(2)+y^(2)=a^(2)` from which two perpendicular tangents can be drawn to parabola `y^(2)=2x`, then find the values of a.

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - `age1//2`
We know that perpendicular tangents intersect on directrix.
So, there exists at least one point on the circle `x^(2)+y^(2)=a^(2)` from which two perpendicular tangents can be drawn to parabola if circle touches or intersects the directrix.
Directrix of the parabola is `x=-1//2`.
`:. "Radius of the circle", age1//2`