class 11

Math

Co-ordinate Geometry

Conic Sections

If a chord, which is not a tangent of the parabola $y_{2}=16x$has the equation $2x+y=p,$and midpoint $(h,k),$then which of the following is(are) possible values (s) of $p,handk?$$p=−1,h=1,k=−3$ $p=2,h=3,k=−4$ $p=−2,h=2,k=−4$ $p=5,h=4,k=−3$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

If $(b_{2}−b_{1})(b_{3}−b_{1})+(a_{2}−a_{1})(a_{3}−a_{1})=0$ , then prove that the circumcenter of the triangle having vertices $(a_{1},b_{1}),(a_{2},b_{2})$ and $(a_{3},b_{3})$ is $(2a_{2+a_{3}} ,2b_{2+}b_{3} )$

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

If two equal chords of a circle intersect within the circle, prove that the segments ofone chord are equal to corresponding segments of the other chord.

Find the equation of the circle with centre :(0, 2) and radius 2

Find the equation to which the equation $x_{2}+7xy−2y_{2}+17x−26y−60=0$ is transformed if the origin is shifted to the point $(2,−3),$ the axes remaining parallel to the original axies.

Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0); focus $(2,0)$

Find the equations of the hyperbola satisfying the given conditions :Foci $(0,±10 )$, passing through (2,3)

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.$25x_{2} +100y_{2} =1$