class 11

Math

Co-ordinate Geometry

Conic Sections

Find common tangent of the two curve $y_{2}=4x$ and $x_{2}+y_{2}−6x=0$ (a) $y=3x +3$ (b) $y=(3 x −3 )$ (c) $y=3x −3$ (d) $y=(3 x +3 )$

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If the chord joining points $P(α)andQ(β)$ on the ellipse $(a_{2}x_{2} )+(b_{2}y_{2} )=1$ subtends a right angle at the vertex $A(a,0),$ then prove that $tan(2a )tan(2β )=−a_{2}b_{2} ˙$

An arch is in the form of a parabola with its axis vertical. The arch is $10$ m high and $5$ m wide at the base. How wide is it $2$ m form the vertex of the parabola?

A line passing through the origin $O(0,0)$ intersects two concentric circles of radii $aandb$ at $PandQ,$ If the lines parallel to the X-and Y-axes through $QandP,$ respectively, meet at point $R,$ then find the locus of $R˙$

If $ω$ is one of the angles between the normals to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at the point whose eccentric angles are $θ$ and $2π +θ$ , then prove that $sin2θ2cotω =1−e_{2} e_{2} $

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is $21 ,$ then find the locus of the focus.

Find the equation of the circle with centre $(−2,3)$ and radius $4$

Find the maximum area of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ which touches the line $y=3x+2.$

A tangent is drawn to the ellipse to cut the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and to cut the ellipse $c_{2}x_{2} +d_{2}y_{2} =1$ at the points P and Q. If the tangents are at right angles, then the value of $(c_{2}a_{2} )+(d_{2}b_{2} )$ is