The tangent at a point P(acosφ,bsinφ) of the ellipse a2x2+b2y2=1 meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.
A beam is supported at its ends by supports which are 12 metres apart. Since the load is connected at its centre, there is a deflection f 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
The line joining the points (x,2x)and(3,5) makes an obtuse angle with the positive direction of the x-axis. Then find the values of x˙
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.
A straight line is drawn through P(3,4) to meet the axis of x and y at AandB , respectively. If the rectangle OACB is completed, then find the locus of C˙