State whether the statements True or False. JustifyThe line 2x + 3y =

1.	State whether the statements True or False. JustifyThe line 2x + 3y = 12 touches the ellipse x2/9 + y2/4 = 2 at the point (3, 2).
Answer» 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

State whether the statements True or False. JustifyThe line 2x + 3y = 12 touches the ellipse x2/9 + y2/4 = 2 at the point (3, 2).

Answer»

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