NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 6
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State Whether the Statements in Examples 17 and 18 Are Correct or Not. Justify
Question 17:
Circle on which the coordinates of any point are where is parameter is given by .
Answer:
True. From given conditions, we have
and
Squaring
And adding, we get .
Question 18:
A bar of given length moves with its extremities on two fixed straight lines at right angles. Any point of the bar describes an ellipse.

Any Point of the Bar Describes an Ellipse
Answer:
True. Let P (x, y) be any point on the bar such that PA = a and PB = b, clearly from the Fig. 11.13.
These give , which is an ellipse
Fill in the Blanks in Examples 19 to 23
Question 19:
The equation of the circle which passes through the point and has its centre at is ________________ .
Answer:
As the circle is passing through the point and its centre is so its radius is . Therefore the required answer is .
Question 20:
A circle has radius 3 units and its centre lies on the line . If it passes through the point , its equation is ________________ .
Answer:
Let be the centre of the circle. Then . Therefore, the equation of the circle is given by
Given that the circle passes through the point and hence we get
Or
Or
Which gives
Therefore, the required equations of the circles are
or
Question 21:
If the latus rectum of an ellipse with axis along x-axis and centre at origin is , distance between length of minor axis, then the equation of the ellipse is ________________ .
Answer:
Given that
Again, we know that
Or
Thus
Again
Or Thus we get
Therefore, the required equation of the ellipse is
Question 22:
The equation of the parabola whose focus is the point and directrix is the line is ________________ .
Answer:
Using the definition of parabola, we have
Squaring, we get
or