Q39 of 63 Page 202

State whether the statements True or False. Justify

The line 2x + 3y = 12 touches the ellipse at the point (3, 2).

4x2 + 9y2 = 72 & 2x + 3y = 12


Solving both the expressions,


2x = 12 – 3y


Squaring both sides,


(2x)2 = (12 – 3y)2


4x2 = (12 – 3y)2


Putting the value of 4x2,


(12 – 3y)2 + 9y2 = 72


144 + 9y2 - 72y + 9y2 - 72 = 0


18y2 - 72y + 72 = 0


Y2 - 4y + 4 = 0


(y – 2)2= 0


y = 2


2x = 12 – 3y


2x = 12 – 3(2)


2x = 12 – 6 = 6


x = 3


So, the point of intersection is (3,2).


TRUE


More from this chapter

All 63 →
37

State whether the statements True or False. Justify

The line lx + my + n = 0 will touch the parabola y2 = 4ax if ln = am2.

 38

State whether the statements True or False. Justify

If P is a point on the ellipse whose foci are S and S′, then PS + PS′ = 8.

 40

State whether the statements True or False. Justify

The locus of the point of intersection of lines and for different value of k is a hyperbola whose eccentricity is 2.

 41

Fill in the Blanks

The equation of the circle having centre at (3, – 4) and touching the line5x + 12y – 12 = 0 is ______.