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: