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˙
What does the equation 2x2+4xy−5y2+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 450 with the old axes?
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
XYand XprimeYprimeare two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XYat A and XprimeYprimeat B. Prove that ∠AOB = 90o