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Tangents on Ellipse Video Lecture | Mathematics (Maths) for JEE Main & Advanced

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FAQs on Tangents on Ellipse Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is the equation of the tangent to an ellipse at a given point?
Ans. The equation of the tangent to an ellipse at a given point (x₁, y₁) is given by: (xx₁) / a² + (yy₁) / b² = 1.
2. How do you find the point of tangency on an ellipse?
Ans. To find the point of tangency on an ellipse, first differentiate the equation of the ellipse with respect to x. Then, substitute the x-coordinate of the point of tangency into the derivative to find the corresponding y-coordinate.
3. Can a tangent to an ellipse be vertical or horizontal?
Ans. Yes, a tangent to an ellipse can be vertical or horizontal depending on the orientation of the ellipse. A vertical tangent occurs when the ellipse is taller than it is wide, while a horizontal tangent occurs when the ellipse is wider than it is tall.
4. How many tangents can be drawn to an ellipse from a point outside the ellipse?
Ans. There can be two tangents drawn to an ellipse from a point outside the ellipse. These tangents are always symmetrical with respect to the major axis of the ellipse.
5. What is the geometric interpretation of a tangent to an ellipse?
Ans. The tangent to an ellipse at a given point represents a line that just touches the ellipse at that point without intersecting it. This line is perpendicular to the radius of the ellipse at that point.
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