If the line x – 1 = 0 is a directrix of the hyperbola kx2 – y2 = 6, then the hyperbola passes through the point
The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is\((2, a),−\frac{1}{2}<a<2 \)then p is equal to _______.
Let Q and R be two points on the line \(\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}\) at a distance \(\sqrt{26}\) from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .
If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t),
\(y=12(1+sint)^2,0<t<\frac{π}{2}, \)
with the positive x-axis is π/3, then y0 is equal to
Read the following passage and the question below. Choose the correct answer. Gandhi never contented himself with large political or economic solutions. He saw the cultural and social backwardness in the Champaran villages and wanted to do something about it immediately. He appealed to teachers. Which of the following statements is true about the passage?
