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Q1. A beam is supported at its ends by supports which are 14 cm apart. Since the load is concentrated at its centre, there is a deflection of 5 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 2 cm?

Solution

Q2. Find the centre and radius of the circle given by the equation (x + 5)² + (y + 1 )² = 9

Solution

Comparing to the standard equation of the circle (x - h)² + (y - k)² = r². We have centre (-5,-1) and radius r = 3.

Q3. Find the equation of the parabola with V(0,0) and focus (0,-2).

Solution

The vertex is the origin and the focus is (0,-2) which lies on the y - axis. Here a = -2, hence the parabola is of the form x² = -4ay.Hence the equation of the parabola is x² = -8y.Alert !  The negative sign is the formula x² = -4ay signifies that it is a downwoard parabola. Take a = 2, as the negative sigin is already considered in the formula.

Q4. Find the equation of the parabola with vertex (0,0) and focus (-5,0).

Solution

The vertex is the origin and the focus is (-5,0) which lies on the x axis. Since a = -5, it is of the form y² = -4ax. Hence the equation of the parabola is y² = -20x.Alert 1. The negative sign in the equation y² = -4ax signifies that it is a left handed parabola. Take a as 5 only as the negative sign is aleady considered in the formula.

Q5. Examine whether the points (2,3)  lies inside, outside or on the circle x² + y² + 2x + 2y - 7 = 0.

Solution

The equation of the circle is x² + y² + 2x + 2y - 7 = 0Substituting the point (2,3) in the equation of the circle we get 4 + 9 + 4 + 6 - 7 = 16 > 0Hence the point lies outside the circle.

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