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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 directrics
- length of the latus rectum
- distance between focii
- distance between directrices of the ellipse:
3x2 + 4y2 = 12
Find the equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.
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 passing through the points (−3, 1) and (2, −2)
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 x – y = 5 is a tangent to the ellipse 9x2 + 16y2 = 144. Find the point of contact
Determine whether the line `x + 3ysqrt(2)` = 9 is a tangent to the ellipse `x^2/9 + y^2/4` = 1. If so, find the co-ordinates of the pt of contact
Find the equation of the tangent to the ellipse `x^2/5 + y^2/4` = 1 passing through the point (2, –2)
Find the equation of the tangent to the ellipse 4x2 + 7y2 = 28 from the point (3, –2).
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 = 20, ⊥ to the line 4x + 3y = 7.
Find the equation of the locus of a point the tangents form which to the ellipse 3x2 + 5y2 = 15 are at right angles
P and Q are two points on the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 with eccentric angles θ1 and θ2. Find the equation of the locus of the point of intersection of the tangents at P and Q if θ1 + θ2 = `π/2`.
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:
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)
If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to ______.
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 eccentricity, foci and the length of the latus rectum of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 are respectively equal to ______.
Tangents are drawn from a point on the circle x2 + y2 = 25 to the ellipse 9x2 + 16y2 – 144 = 0 then find the angle between the tangents.
If the chord through the points whose eccentric angles are α and β on the ellipse `x^2/a^2 + y^2/b^2` = 1 passes through the focus (ae, 0), then the value of tan `α/2 tan β/2` will be ______.
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 ______.
Let the eccentricity of an ellipse `x^2/a^2 + y^2/b^2` = 1, a > b, be `1/4`. If this ellipse passes through the point ```(-4sqrt(2/5), 3)`, then a2 + b2 is equal to ______.
If P1 and P2 are two points on the ellipse `x^2/4 + y^2` = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 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______.
If the length of the major axis of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] is three times the length of minor axis, then its eccentricity 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______.
Eccentricity of the conic \[16x^2+7y^2=112\] is______.
For the ellipse \[3x^2+4y^2=12,\] the length of latus rectum is______.
