The points of contact of the tangents drawn from P(-2,2) to the parabola y^2=16 x are A and B. T

step 1 So in this question, L is equal to root S1, S1 that is equal to, that is equal to root 16, that

The points of contact of the tangents drawn from P(-2,2) to...

The points of contact of the tangents drawn from $\mathrm{P}(-2,2)$ to the parabola $\mathrm{y}^{2}=16 \mathrm{x}$ are $\mathrm{A}$ and $\mathrm{B}$. Then $\mathrm{AB}$ is
(a) $4 \sqrt{17}$
(b) $\sqrt{5}$
(c) $2 \sqrt{17}$
(d) $3 \sqrt{17}$

Key Concepts

Parametric Representation of a Parabola

This concept involves expressing the coordinates of points on a parabola using a parameter, which simplifies the derivation of tangents and related equations. Parametrization helps in managing complex algebraic manipulations by reducing the variables involved, making it easier to find points of contact of tangents drawn from an external point.

Distance Formula

The distance formula is derived from the Pythagorean theorem and is used to calculate the distance between two points in the plane. In analytic geometry, it is essential for determining the length of line segments, such as the chord of contact or any other segment connecting two points obtained from geometric constructions.

Tangent to a Parabola

A tangent to a parabola is a line that touches the curve at exactly one point, without crossing it. In analytic geometry, the tangent can be derived by setting the line and the curve equations to have exactly one point of intersection, which often leads to a condition involving the discriminant. This concept is fundamental when analyzing the relationship between lines and conic sections.

Chord of Contact

The chord of contact is the line segment connecting the points where two tangents drawn from an external point meet the conic section. It effectively represents the envelope of the contact points and is a useful construct in solving problems related to tangents and their geometric properties on conic sections.

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