NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 7

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Question 23:

The eccentricity of the hyperbola which passes through the points and is ________________ .

Answer:

Given that the hyperbola is passing through the points and , so we get and .

Again, we know that . This gives

Or

Or.

11.3 EXERCISE

Short Answer Type

Question 1:

Find the equation of the circle which touches the both axes in first quadrant and whose radius is a.

Answer:

Question 2:

Show that the point given by and lies on a circle for all real values of t such that where a is any given real numbers.

Answer:

Squaring both the equations,

Adding both the equations,

The equation of a circle having centre , having radius as “” units, is

Centre Radius units

Hence proved

Question 3:

If a circle passes through the point then find the coordinates of its centre.

Answer:

Question 4:

Find the equation of the circle which touches x-axis and whose centre is .

Answer:

Question 5:

If the lines and are tangents to a circle, then find the radius of the circle.

[Hint: Distance between given parallel lines gives the diameter of the circle.]

Answer:

Question 6:

Find the equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant.

[Hint: Let be the radius of the circle, then will be centre and perpendicular distance from the centre to the given line gives the radius of the circle.]

Answer:

Question 7:

If one end of a diameter of the circle is , then find the coordinate of the other end of the diameter.

Answer:

Question 8:

Find the equation of the circle having as its centre and passing through

Answer: