Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2).

OR

P (-2, 5) and Q (3, 2) are two points. Find the co-ordinates of the point R on PQ such that PR=2QR.

Case Study Based- 3

Applications of Parabolas-Highway Overpasses/Underpasses

A highway underpass is parabolic in shape.

Parabola

A parabola is the graph that results from p(x)=ax²+bx+c

Parabolas are symmetric about a vertical line known as the Axis of Symmetry.

The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the Vertex

(a) If the highway overpass is represented by x² – 2x – 8. Then its zeroes are

(i) (2,-4) (ii) (4,-2) (iii) (-2,-2) (iv) (-4,-4)

(b) The highway overpass is represented graphically.

Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial

(i) Intersects x-axis

(ii) Intersects y-axis

(iii) Intersects y-axis or x-axis

(iv)None of the above

(c) Graph of a quadratic polynomial is a

(i) straight line

(ii) circle

(iii)parabola

(iv)ellipse

(d) The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is

(i) x² – 6x + 2

(ii) x² – 36

(iii)x² – 6

(iv)x² – 3

(e) The number of real zeroes that polynomial f(x) = (x – 2)² + 4 can have is:

(i)1

(ii) 2

(iii) 0

(iv) 3

3 bells ring at an interval of 4,7 and 14 minutes. All three bell rang at 6 am, when the three balls will the ring together next?

Draw a line segment PQ of length 9cm. With P and Q as centres, draw circles of radius 5cm and 3cm respectively. Construct tangents to each circle from the centre of the other circle.

If tanA = 3/4, find the value of 1/sinA + 1/cosA

OR

If √3 sinƟ-cosƟ=0 and 0°<Ɵ <90°, find the value of Ɵ