Coordinate Geom...

Let P and Q be points $$(4, 4)$$ and $$(9, 6)$$ of parabola $${y^2} = 4a\left( {x - b} \right)$$ If R be a point on the arc of the parabola between P and Q, such that the area of  $$\Delta PRQ$$ is largest, then R is

The perpendicular bisector of the line segment joining the point A ( 1,5 ) and B ( 4,6 ) cuts the Y axis at

Area of the triangle formed by $${ (x }_{ 1 },{ y }_{ 1 })$$,$${ (x }_{ 2 },{ y }_{ 2 })$$,
$${ (3x }_{ 2 }-{ 2x }_{ 1 },{ 3y }_{ 2 }-{ 2y }_{ 1 })$$ is

The area of a triangle whose sides are $$ a , b $$ and $$ c $$ is

The arrangement of the areas of the triangles formed by the following points in ascending order is 
i) P(0,0), Q(4,0), R(0,3)
ii) P(0,0), Q(5,0), R(0,2)
iii) P(0,0), Q(0,5), R(6,0)
iv) p(3,0), Q(0,6), R(0,0)

Area of the triangle formed by co-ordinate axes and the line x + y = 5 is

The centre of the circle which passes through A ($$\alpha, 0$$), B (0, $$\beta$$), C (0, 0) is

two medians drawn from the acute angles of a right angled  triangle interect at the angle $$\pi /6$$ if thelength the hypotenuse of the triangle is 3 units then the area of the triangle is

If $$m_1$$ and $$m_2$$ are the roots of the equation $$x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0 $$, then the area of the triangle formed by the lines $$y=m_1x,y=-m_2x$$ and $$y=1$$ is:

The area inside the parabola $$5x^2 - y = 0 $$ but outside the parabola $$2x^2 - y + 9 = 0$$ is