class 11

Math

Co-ordinate Geometry

Conic Sections

The equation of a tangent to the parabola $y_{2}=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

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An ellipse has $OB$ as the semi-minor axis, $FandF_{′}$ as its foci, and $∠FBF_{′}$ a right angle. Then, find the eccentricity of the ellipse.

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle $x_{2}+(y−1)_{2}=2$. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that $PQ=PR=322 $.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

Find the equation of the hyperbola satisfying the given conditions: Foci $(±35 ,0)$ the latus rectum is of length $8$

Find the lengths of the major and minor axes and the eccentricity of the ellipse $16(3x−4y+2)_{2} +9(4x+3y−5)_{2} =1$

If the equation $(5x−1)_{2}+(5y−2)_{2}=(λ_{2}−2λ+1)(3x+4y−1)_{2}$ represents an ellipse, then find values of $λ˙$

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1.$

Find the equation of the circle with radius $5$ whose centre lies on $x$-axis and passes through the point $(2,3)$

An arc of a bridge is semi-elliptical with the major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then prove that the best approximation of the height of the acr 2 m from the center of the base is $38 m˙$