Circumcentre

Q. P(t1) and P(t2) are the points t1and t2 on the parabola }y^2=4ax . The normals at }P and }Q meet on } the parabola. Show that the middle point of }PQ lies on the }{ parabola }y^2=2a(x+2a) .

Q. Circumcentre of a triangle, which is formed by the lines y=x, y=2x and y= 3x+4 is

1. (6, 8)
2. (6, -8)
3. (3, 4)
4. (-3, -4)

Q.

A line passes through $(x_1,y_1)$ and (h, k). If slope of the line is m, show that $k-y_1=m(h-x_1)$.

Q.

Which of the following statements is/are correct statements?
1. Centroid of a triangle is the point of concurrency of medians
2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle
3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle
4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side
5. A triangle can have only one excentre

1. only 1, 4, 5

2. All 1, 2, 3, 4, 5

3. only 1, 2, 3, 4

4. only 1, 4