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Algebra
Sets and RelationsLogarithmsQuadratic EquationsSequences and SeriesPermutations and CombinationsProbabilityBinomial TheoremVector AlgebraThree Dimensional GeometryMatrices and DeterminantsStatisticsMathematical ReasoningComplex Numbers
Trigonometry
Trigonometric Ratios & IdentitiesTrigonometric EquationsInverse Trigonometric FunctionsProperties of Triangles
Calculus
FunctionsLimits, Continuity and DifferentiabilityDifferentiationApplication of DerivativesIndefinite IntegrationDefinite IntegrationArea Under The CurvesDifferential Equations
Coordinate Geometry
Straight Lines and Pair of Straight LinesCircleParabolaEllipseHyperbola
Ellipse
Practice Questions
MCQ (Single Correct Answer)
1
Let $T_1$ be the tangent drawn at a point $P(\sqrt{2}, \sqrt{3})$ on the ellipse $\frac{x^2}{4}+\frac{y^2}{6}=1$. If ( $\alpha, \beta$ ) is the point where, $T_1$ intersects another tangent $T_2$ to the ellipse perpendicularly, then $\alpha^2+\beta^2$ is equal to
AP EAPCET 2024 - 23th May Morning Shift
2
The length of the latusrectum of $16 x^2+25 y^2=400$ is
AP EAPCET 2024 - 22th May Evening Shift
3
The product of perpendiculars from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ on the tangent at any point on the ellipse is
AP EAPCET 2024 - 21th May Evening Shift
4
If $A_1, A_2, A_3$ are the areas of ellipse $x^2+4 y^2-4=0$ its director circle and auxiliary circle respectively, then $A_2+A_3-A_1=$
AP EAPCET 2024 - 21th May Morning Shift
5
If the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ having $(1,1)$ as its middle point is $x+\alpha y=\beta$, then
AP EAPCET 2024 - 20th May Evening Shift
6
Let F and $F^1$ be the foci of the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1(b<2)$ and $B$ is one end of the minor axis. If the area of the triangle $\mathrm{FBF}^1$ is $\sqrt{3}$ sq units, then the eccentricity of the ellipse is
AP EAPCET 2024 - 20th May Morning Shift
7
If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ touches the circle $x^2+y^2=4$, then maximum value of $a b$ is
AP EAPCET 2024 - 19th May Evening Shift
8
If $4 x-3 y-5=0$ is a normal to the ellipse $3 x^2+8 y^2=k$, then the equation of the tangent drawn to this ellipse at the point $(-2, m)(m>0)$ is
AP EAPCET 2024 - 18th May Morning Shift
9

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ is $$90^{\circ}$$, then it eccentricity

AP EAPCET 2022 - 5th July Morning Shift
10

The focal distances of the point $$\left(\frac{4}{\sqrt{5}}, \frac{3}{\sqrt{5}}\right)$$ on the ellipse $$\frac{x^2}{4}+\frac{y^2}{9}=1$$ are

AP EAPCET 2022 - 4th July Evening Shift
11

A stick of length $$r$$ units slides with its ends on coordinate axes. Then, the locus of the mid-point of the stick is a curve whose length is

AP EAPCET 2022 - 4th July Morning Shift
12

The eccentric angle of a point on the ellipse $$x^2+3 y^2=6$$ lying at a distance of 2 units from its centre is

AP EAPCET 2022 - 4th July Morning Shift
13

If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ will subtend a right angle at

AP EAPCET 2021 - 20th August Morning Shift
14

In an ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is

AP EAPCET 2021 - 19th August Evening Shift
15

If a point $$P(x, y)$$ moves along the ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$ and if $$C$$ is the center of the ellipse, then the sum of maximum and minimum values of $$C P$$ is

AP EAPCET 2021 - 19th August Morning Shift