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Parametric Equation of a Circle

The line 2x+y...

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{ The line }2x+y=3 cuts the ellipse }4x^2+y^2=5}{ at }P and }Q . If }θ be the angle between the normals }}{ at these points, then tan }θ is equal to

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2 x + y = 3

cuts the ellipse

4 x^{2} + y^{2} = 5

P

Q

θ

is the angle between normals at

P

Q

tan θ =

P Q

be a focal chord of the parabola

y^{2} = 4 a x

. The tangents to the parabola at

P

Q

meet at a point lying on the line

y = 2 x + a, a > 0

P Q

subtends an angle

θ

at the vertex of

y^{2} = 4 a x

θ

Q. If the acute angles between the curves

y = | x^{2} - 1 |

y = | x^{2} - 3 |

at their points of intersection be

θ

tan θ = \frac{m}{7}

m^{2}

Q. The tangent at a point P(

θ

) to the elllipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

cuts the auxiliary circle at point

Q

R

Q R

subtends a right angle at the centre

C

of the ellipse, then the eccentricity of the ellipse is:

Q. Find where the line

2 x + y = 3

4 x^{2} + y^{2} = 5.

Obtain the equations of the normals at the points of intersection and determine the co-ordinates of the point where these normals cut each other.

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Parametric Equation of a Circle

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