Mathematics Test 15

Result

Mathematics Test 15

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Weekly Quiz Competition

Question 1
4 / -1

The lines 2x − 3y = 5 and 3x − 4y = 7 are diameters of a circle having area as 154 sq units. Then the equation of the circle is

A
x² + y² + 2x − 2y = 62

B
x² + y² + 2x − 2y = 47

C
x² + y² − 2x + 2y = 47

D
x² + y² − 2x + 2y = 62

Solution

Intersection of diameter is the point (1, − 1)
πs² = 154
⇒ s² = 49
(x − 1)² + (y + 1)² = 49
Question 2
4 / -1

The degree and order of the differential equation of the family of all parabolas whose axis is x−axis, are respectively

A
2, 1

B
1, 2

C
3, 2

D
2, 3

Solution

Equation y² = 4a (x − h)
2yy₁ = 4a ⇒ yy₁ = 2a
yy₂ = y₁² = 0.