The equation of a tangent to the ellipse 2 x^2+7 y^2=14, drawn from the point (5,2) is (a) x-9 y

step 1 So, we know that the equation of tangent for this standard circle is given by this formula. In t

The equation of a tangent to the ellipse 2 x^2+7 y^2=14,...

Key Concepts

Tangents from an External Point

When drawing tangents from a point external to a conic section, the line must not only satisfy the tangency condition but also pass through the given point. This involves solving for the line parameters such that both the external point condition and the zero-discriminant condition are met.

Condition for Tangency

For a line to be tangent to a conic section, substituting the line’s equation into the conic's equation must yield a quadratic equation with a discriminant equal to zero. This zero discriminant ensures that there is exactly one intersection point between the line and the conic.

Ellipse

An ellipse is a conic section defined by a quadratic equation in two variables. Its equation can be written in standard form, which highlights its principal axes and symmetry. Understanding the properties of ellipses is fundamental for analyzing curves and their tangents.

Tangent Line

A tangent line to a curve is a straight line that touches the curve at exactly one point without crossing it, representing the direction in which the curve is heading at that point. In conic sections, tangents are used to study properties such as slopes and points of contact.

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