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प्रश्न
Select the correct option from the given alternatives:
The equation of the ellipse having eccentricity `sqrt(3)/2` and passing through (− 8, 3) is
पर्याय
4x2 + y2 = 4
x2 + 4y2 = 100
4x2 + y2 = 100
x2 + 4y2 = 4
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उत्तर
The equation of the ellipse having eccentricity `sqrt(3)/2` and passing through (− 8, 3) is x2 + 4y2 = 100
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संबंधित प्रश्न
Find the
- lengths of the principal axes.
- co-ordinates of the focii
- equations of directrices
- length of the latus rectum
- distance between focii
- distance between directrices of the ellipse:
3x2 + 4y2 = 1
Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6
Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.
Find the equation of the ellipse in standard form if the distance between foci is 6 and the distance between directrix is `50/3`.
Find the equation of the ellipse in standard form if the latus rectum has length of 6 and foci are (±2, 0).
Find the equation of the ellipse in standard form if the dist. between its directrix is 10 and which passes through `(-sqrt(5), 2)`.
Find the equation of the ellipse in standard form if eccentricity is `2/3` and passes through `(2, −5/3)`.
Find the eccentricity of an ellipse, if the length of its latus rectum is one-third of its minor axis.
Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci
Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16
A tangent having slope `–1/2` to the ellipse 3x2 + 4y2 = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle
Show that the line 8y + x = 17 touches the ellipse x2 + 4y2 = 17. Find the point of contact
Find the equation of the tangent to the ellipse 2x2 + y2 = 6 from the point (2, 1).
Find the equation of the tangent to the ellipse x2 + 4y2 = 9 which are parallel to the line 2x + 3y – 5 = 0.
Find the equation of the tangent to the ellipse 5x2 + 9y2 = 45 which are ⊥ to the line 3x + 2y + y = 0.
Find the equation of the tangent to the ellipse x2 + 4y2 = 20, ⊥ to the line 4x + 3y = 7.
The eccentric angles of two points P and Q the ellipse 4x2 + y2 = 4 differ by `(2pi)/3`. Show that the locus of the point of intersection of the tangents at P and Q is the ellipse 4x2 + y2 = 16
Find the equations of the tangents to the ellipse `x^2/16 + y^2/9` = 1, making equal intercepts on co-ordinate axes
Select the correct option from the given alternatives:
If the line 4x − 3y + k = 0 touches the ellipse 5x2 + 9y2 = 45 then the value of k is
Select the correct option from the given alternatives:
The equation of the tangent to the ellipse 4x2 + 9y2 = 36 which is perpendicular to the 3x + 4y = 17 is,
Select the correct option from the given alternatives:
Centre of the ellipse 9x2 + 5y2 − 36x − 50y − 164 = 0 is at
Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8
Answer the following:
Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)
On the ellipse `x^2/8 + "y"^2/4` = 1 let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 – e2). A is ______.
The tangent and the normal at a point P on an ellipse `x^2/a^2 + y^2/b^2` = 1 meet its major axis in T and T' so that TT' = a then e2cos2θ + cosθ (where e is the eccentricity of the ellipse) is equal to ______.
The normal to the ellipse `x^2/a^2 + y^2/b^2` = 1 at a point P(x1, y1) on it, meets the x-axis in G. PN is perpendicular to OX, where O is origin. Then value of ℓ(OG)/ℓ(ON) is ______.
The point on the ellipse x2 + 2y2 = 6 closest to the line x + y = 7 is (a, b). The value of (a + b) will be ______.
Eccentricity of ellipse `x^2/a^2 + y^2/b^2` = 1, if it passes through point (9, 5) and (12, 4) is ______.
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.
The locus of a variable point whose distance from (- 2, 0) is \[\frac{2}{3}\] times its distance from the line \[x=-\frac{9}{2}\], is______.
The distance of the point \[^{\prime}\theta^{\prime}\] on the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] from a focus is______.
\[\frac{x^{2}}{r^{2}-r-6}+\frac{y^{2}}{r^{2}-6r+5}=1\] will represent the ellipse, if r lies in the interval______.
The distance between the foci of the ellipse \[3x^2+4y^2=48\] is______.
