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Verify that the point P(a cos 0, bsin 0) lies on the ellipse 1, %3D where a and b are the semi-major and semi-minor axes respectively of the ellipse. Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is az sin 0 – by cos 0 = (a? – b2) sin 0 cos 0. If P is not on the axes and if the normal at P passes through the point B(0,6), Show that a? > 262. If further, the tangent at P meets the y-axis at Q, show that Nth CamScannetmScanner a? |BQ| = h2

Verify that the point P(a cos 0, bsin 0) lies on the ellipse 1, %3D where a and b are the semi-major and semi-minor axes respectively of the ellipse. Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is az sin 0 – by cos 0 = (a? – b2) sin 0 cos 0. If P is not on the axes and if the normal at P passes through the point B(0,6), Show that a? > 262. If further, the tangent at P meets the y-axis at Q, show that Nth CamScannetmScanner a? |BQ| = h2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 31E
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Verify that the point P(a cos 0, bsin 0) lies on the ellipse 1, %3D where a and b are the semi-major and semi-minor axes respectively of the ellipse. Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is az sin 0 – by cos 0 = (a? – b2) sin 0 cos 0. If P is not on the axes and if the normal at P passes through the point B(0,6), Show that a? > 262. If further, the tangent at P meets the y-axis at Q, show that Nth CamScannetmScanner a? |BQ| = h2
Transcribed Image Text:Verify that the point P(a cos 0, bsin 0) lies on the ellipse 1, %3D where a and b are the semi-major and semi-minor axes respectively of the ellipse. Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is az sin 0 – by cos 0 = (a? – b2) sin 0 cos 0. If P is not on the axes and if the normal at P passes through the point B(0,6), Show that a? > 262. If further, the tangent at P meets the y-axis at Q, show that Nth CamScannetmScanner a? |BQ| = h2
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