1
If parabola y² = qx and 25[(x - 3)² + (y+2)²] = (3x-4y-2)² are equal, then value of q is ...
2
If the segment intercepted by the parabola y = 4ax with the line lx+my+n=0 subtends a right angle at ...
3
The graph of the curve x² + y²-2xy-8x-8y+32=0 falls wholly in the ...
4
A point P(x, y) moves in xy plane such that x = a cos² θ and y = 2a sin θ, where θ is a parameter. T ...
5
Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of the midpoint of PQ is ...
6
P(x, y) is a variable point on the parabola y² = 4ax and Q(x+c, y+c) is another variable point, wher ...
7
AB is a chord of the parabola y² = 4ax with vertex A. BC is drawn perpendicular to AB meeting the ax ...
8
A line L passing through the focus of the parabola y² = 4(x-1) intersects the parabola in two distin ...
9
If PSQ is the focal chord of the parabola y² = 8x such that SP=6. Then the length of SQ is ...
10
The circle x² + y² + 2λx = 0, touches the parabola y² = 4x externally. Then ...
11
An equilateral triangle SAB is inscribed in the parabola y^2 = 4ax having its focus at 'S'. If chord ...
12
C is the centre of the circle with centre (0, 1) and radius unity. P is the parabola y = ax². The se ...
13
The length of the chord of the parabola y² = x which is bisected at the point (2, 1) is ...
14
If A1B1 and A2B2' are two focal chords of the parabola y² = 4ax, then the chords A1'A2' and B1'B2' i ...
15
Set of values of a for which the point (a, 1) lies inside the curves x^2 + y^2 - 4 = 0 and y^2 = 4x ...
16
The curve represented by the equation √px+√qy = 1, where p, q ∈ R, p, q>0 is ...
17
A water jet from a fountain reaches its maximum height of 4 m at a distance 0.5 m from the vertical ...
18
If (a, b) is the midpoint of a chord passing through the vertex of the parabola y² = 4x, then ...
19
A set of parallel chords of the parabola y² = 4ax have their midpoints on ...
20
If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas ...
21
Let y = f(x) be a parabola, having its axis parallel to y-axis, which is touched by the line y = x a ...
22
Let S be the focus of y² = 4x and a point P is moving on the curve such that its abscissa is increas ...
23
Two parabolas have the same focus. If their directrices are the x-axis and the y-axis, respectively, ...
24
If a and C are the lengths of segments of any focal chord of the parabola y² = 2bx (b>0), then the r ...
25
If P be a point on the parabola y² = 3(2x - 3) and M is the foot of perpendicular drawn from P on th ...
26
If y = mx + c touches the parabola y² = 4a(x + a), then ...
27
The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x-y+1= ...
28
Vertex of the parabola whose parametric equation is x=t²-t+1, y=t²+1+t; t ∈ R, is ...
29
The ratio in which the line segment joining the points (4,-6) and (3, 1) is divided by the parabola ...
30
Parabolas y² = 4a(x - c1) and x² = 4a(y - c2), where c₁ and c₂ are variable, are such that they touc ...
31
The locus of a point on the variable parabola y² = 4ax, whose distance from focus is always equal to ...
32
The triangle PQR of area 'A' is inscribed in the parabola y² = 4ax such that the vertex P lies at th ...
