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.

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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