NCERT Class 11-Math՚S: Exemplar Chapter – 11 Conic Sections Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 9:

If the line touches the circle , then find the value of .

[Hint: Equate perpendicular distance from the centre of the circle to its radius] .


Question 10:

Find the equation of a circle concentric with the circle and has double of its area.

[Hint: concentric circles have the same centre.]


Question 11:

If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity


Question 12:

Given the ellipse with equation , find the eccentricity and foci.


Question 13:

If the eccentricity of an ellipse is and the distance between its foci is 10, then find latus rectum of the ellipse.


Question 14:

Find the equation of ellipse whose eccentricity is , latus rectum is 5 and the centre is .


Question 15:

Find the distance between the directrices of the ellipse .


Question 16:

Find the coordinates of a point on the parabola whose focal distance is .


Question 17:

Find the length of the line-segment joining the vertex of the parabola and a point on the parabola where the line-segment makes an angle to the .


Question 18:

If the points and are respectively the vertex and focus of a parabola, then find the equation of the parabola.


Question 19:

If the line is tangent to the parabola then find the value of .

[Hint: Solving the equation of line and parabola, we obtain a quadratic equation and then apply the tangency condition giving the value of ] .


Question 20:

If the distance between the foci of a hyperbola is and its eccentricity is , then obtain the equation of the hyperbola.


Question 21:

Find the eccentricity of the hyperbola .


Question 22:

Find the equation of the hyperbola with eccentricity and foci at .