Mathematics : Conic Section

Check whether the points (2, 2), (4, 4) and  lie inside, outside or on the cirlcle 

The locus of the foot of perpendicular drawn from the centre of the ellipse x²+3y² =6 on any tangent to it is

• (x²-y²)² = 6x²+2y²

• (x²-y²)² = 6x² -2y²

• (x²+y²)² = 6x²+2y²

• (x²+y²)² = 6x²+2y²

The slope of the line touching both the parabolas y² = 4x and x²-32y is 

• 1/2

• 3/2

• 1/8

• 1/8

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

• (-5,2)

• (2,-5)

• (5,-2)

• (5,-2)

The equation of the circle passing through the foci of the ellipse  and having centre at (0,3) is 

• x²+y²-6y-7 =0

• x²+y²-6y+7 =0

• x²+y²-6y-5 =0

• x²+y²-6y-5 =0

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 − T_n = 10, then the value of n is

• 7

• 5

• 10

• 10

Given A circle, 2x² + 2y²= 5 and parabola,  
Statement I An equation of a common tangent to these curves is 
Statement II If the line  is the common tangent, then m satisfies m⁴-3m²+2 =0

• Statement I is true,  Statement II is true; Statement II is a correct explanation for statement I

• Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I

• Statement I is true, Statement II is false

• Statement I is true, Statement II is false

Statement I An equation of a common tangent to the parabola  and the ellipse 2x² +y² =4 is .
Statement II If the line  is a common tangent to the parabola  and the ellipse 2x² +y² =4, then m satisfies m⁴ +2m² =24

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1