Class 12

Math

3D Geometry

Conic Sections

Prove that the area of the triangle whose vertices are $(t,t−2),(t+2,t+2),$ and $(t+3,t)$ is independent of $t˙$

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What does the equation $2x_{2}+4xy−5y_{2}+20x−22y−14=0$ become when referred to the rectangular axes through the point $(−2,−3)$ , the new axes being inclined at an angle at $45_{0}$ with the old axes?

Find the centre and radius of the circles$x_{2}+y_{2}−8x+10y−12=0$

Find the equation of the circle with centre : $(−a,b)$and radius $a_{2}−b_{2} $.

Write True or False: Give reasons for your answers.(i) Line segment joining the centre to any point on the circle is a radius of the circle.(ii) A circle has only finite number of equal chords.(iii) If a circle is divided into three equal arcs, each is a major arc.(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.(v) Sector is the region between the chord and its corresponding arc.(vi) A circle is a plane figure.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle

$XY$and $XprimeYprime$are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting $XY$at A and $XprimeYprime$at B. Prove that $∠AOB=90o$

Find the equation of the circle with centre :$(21 ,41 )$ and radius $121 $

In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $∠BEC=130o$ and $∠ECD=20⊙$ Find $∠BAC˙$