Advertisements
Advertisements
Question
Find the equation of the parabola with latus-rectum joining points (4, 6) and (4, -2).
Solution
Joining points are (4, 6) and (4, -2)
Length of latus - rectum = 4a
∴ `sqrt((4 - 4)^2 + (6+ 2)^2) = 4a`
⇒ `sqrt((8)^2)` = 4a
∴ 4a = 8
Hence, equation of parabola
Y2 = 4ax
Y2 = 8x
∴ (y -2)2 = 8x
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by the curve \[x = a t^2 , y = 2\text{ at }\]between the ordinates corresponding t = 1 and t = 2.
Find the area of the region in the first quadrant bounded by the parabola y = 4x2 and the lines x = 0, y = 1 and y = 4.
Find the area of the region bounded by x2 = 4ay and its latusrectum.
Calculate the area of the region bounded by the parabolas y2 = x and x2 = y.
Find the area bounded by the curve y = 4 − x2 and the lines y = 0, y = 3.
Find the area of the region \[\left\{ \left( x, y \right): \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \leq \frac{x}{a} + \frac{y}{b} \right\}\]
Using integration, find the area of the triangular region, the equations of whose sides are y = 2x + 1, y = 3x+ 1 and x = 4.
Draw a rough sketch of the region {(x, y) : y2 ≤ 3x, 3x2 + 3y2 ≤ 16} and find the area enclosed by the region using method of integration.
Find the area enclosed by the parabolas y = 5x2 and y = 2x2 + 9.
Find the area of the region bounded by the curves y = x − 1 and (y − 1)2 = 4 (x + 1).
Find the area bounded by the parabola y = 2 − x2 and the straight line y + x = 0.
The area bounded by the parabola y2 = 4ax, latusrectum and x-axis is ___________ .
Area bounded by parabola y2 = x and straight line 2y = x is _________ .
The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is (b −1) sin (3b + 4). Then, f (x) is __________ .
The area bounded by the curve y = x |x| and the ordinates x = −1 and x = 1 is given by
Using the method of integration, find the area of the region bounded by the lines 3x − 2y + 1 = 0, 2x + 3y − 21 = 0 and x − 5y + 9 = 0
Using integration, find the area of the smaller region bounded by the ellipse `"x"^2/9+"y"^2/4=1`and the line `"x"/3+"y"/2=1.`
Find the area of the region bounded by the parabola y2 = 2px, x2 = 2py
Find the area of the region bounded by the curve y2 = 4x, x2 = 4y.
Draw a rough sketch of the given curve y = 1 + |x +1|, x = –3, x = 3, y = 0 and find the area of the region bounded by them, using integration.
The area of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is ______.
The area of the region bounded by the circle x2 + y2 = 1 is ______.
If a and c are positive real numbers and the ellipse `x^2/(4c^2) + y^2/c^2` = 1 has four distinct points in common with the circle `x^2 + y^2 = 9a^2`, then
The area of the region enclosed by the parabola x2 = y, the line y = x + 2 and the x-axis, is
Find the area of the region bounded by `y^2 = 9x, x = 2, x = 4` and the `x`-axis in the first quadrant.
What is the area of the region bounded by the curve `y^2 = 4x` and the line `x` = 3.
Let f : [–2, 3] `rightarrow` [0, ∞) be a continuous function such that f(1 – x) = f(x) for all x ∈ [–2, 3]. If R1 is the numerical value of the area of the region bounded by y = f(x), x = –2, x = 3 and the axis of x and R2 = `int_-2^3 xf(x)dx`, then ______.
Let g(x) = cosx2, f(x) = `sqrt(x)`, and α, β (α < β) be the roots of the quadratic equation 18x2 – 9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0, is ______.
Find the area of the minor segment of the circle x2 + y2 = 4 cut off by the line x = 1, using integration.
