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I need to find the tangent line to an ellipse by only knowing the slope of a parallel line to the tangent line
Equation of ellipse : x²/a² + y²/b² = 1Let the point of tangency, whose coordinates will also satisfy the equation of the tangent line, be (p,q).The slope of the tangent line is equal to the value of the derivative at the point of tangency.Derivating wrt to x,2x/a² + 2yy'/b² = 0y' = -(b²/a²)(x/y) Therefore, evaluating y' when x = p and y = q,m = -(b²/a²)(p/q)Solving for, say, q, we haveq = -(b²/a²)(p/m)Since (p, q) lies on the ellipse, it satisfies the ellipse's equation; thus,p²/a² + q²/b² = 1Substitute for q from the earlier result:p²/a² + [-(b²/a²)(p/m)]²/b² = 1This simplifies to(p²/a²)[1 + (b²/(m²a²))] = 1ThanksBharat BajajIIT delhiaskiitians faculty
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