A point moves in such a way that the difference of its distance from two points (8, 0) and (- 8, 0) always remains 4. Then, the locus of the point is
a circle
a parabola
an ellipse
a hyperbola
The number of integer values of m, for which the x - coordinate of the point of intersection of the lines 3x + 4y= 9 and y =mx + 1 is also an integer, is
0
2
4
1
If a straight line passes through the point () and the portion of the line intercepted between the axes is divided equally at that point, then is
0
1
2
4
Let p, q and r be the altitudes of a triangle with area S and perimeter 2 t. Then, the value of is
Let C1 and C2 denote the centres of the circles x2 + y2 = 4 and (x - 2)2 + y2 = 1 respectively and let P and Q be their points of intersection. Then, the areas of C2PQ and CPQ are in the ratio
3 : 1
5 : 1
7 : 1
9 : 1
A straight line through the point of intersection of the lines x + 2y = 4 and 2x + y = 4 meets the coordinate axes at A and B. The locus of the mid-point of AB is
3(x + y) = 2xy
2(x + y) = 3xy
2(x + y) = xy
x + y = 3xy
B.
2(x + y) = 3xy
Given lines are,
x + 2y = 4 ...(i)
and 2x+ y= 4 ...(ii)
Solving Eqs. (i) and (ii), we get
Meets x - axis at A and y - axis at B.
If the straight line (iii) passes through the point then
Let the mid-point of AB be (h, k).
Replace x, y from h, k respectively, we get required locus
i.e., 2(x + y) 3xy
Let P and Q be the points on the parabola y2 = 4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
1
2
4
6
The incentre of an equilateral triangle is (1, 1) and the equation of one side is 3x + 4y + 3 = 0. Then, the equation of the circumcircle of the triangle is
x2 + y2 - 2x - 2y - 2 = 0
x2 + y2 - 2x - 2y - 14 = 0
x2 + y2 - 2x - 2y + 2 = 0
x2 + y2 - 2x - 2y + 14 = 0