Given the parabola `C : y = x^(2)`. If the circle at y axis with radius 1 touches parabola C at two distinct points, then find the coordinate of the c

Question

Given the parabola `C : y = x^(2)`. If the circle at y axis with radius 1 touches parabola C at two distinct points, then find the coordinate of the c

Given the parabola `C : y = x^(2)`. If the circle at y axis with radius 1 touches parabola C at two distinct points, then find the coordinate of the center of the circle K and the area of the figure surrounded by C and K.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Related Questions

If the x-coordinate of a point `P` on the join of `Q(22,1)a n dR(5,1,-2)i s4,` then find its `z-` coordinate.

2 Answers 4 Views

Let `l_(1) and l_(2)` be the two skew lines. If P, Q are two distinct points on `l_(1)` and R, S are two distinct points on `l_(2)`, then prove that P

2 Answers 6 Views

Find the equation of the parabola which has axis parallel to the y-axis and which passes through the points `(0,2),(-1,0),a n d(1,6)dot`

2 Answers 4 Views

If the chord of contact of tangents from a point `P` to the parabola `y^2=4a x` touches the parabola `x^2=4b y ,` then find the locus of `Pdot`

2 Answers 6 Views

A circle is drawn to pass through the extremities of the latus rectum of the parabola `y^2=8xdot` It is given that this circle also touches the direct

2 Answers 6 Views

A line `L` passing through the focus of the parabola `y^2=4(x-1)` intersects the parabola at two distinct points. If `m` is the slope of the line `L ,

2 Answers 4 Views

Two mutually perpendicular tangents of the parabola `y^(2)=4ax` meet the axis at `P_(1)andP_(2)`. If S is the focal of the parabola, Then `(1)/(SP_(1)

2 Answers 6 Views

`P ,Q ,` and `R` are the feet of the normals drawn to a parabola `(y-3)^2=8(x-2)` . A circle cuts the above parabola at points `P ,Q ,R ,a n dS` . The

2 Answers 5 Views

Tangent to the parabola `y=x^(2)+ax+1` at the point of intersection of the y-axis also touches the circle `x^(2)+y^(2)=r^(2)`. Also, no point of the p

2 Answers 6 Views

Points A, B, C lie on the parabola `y^2=4ax` The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the

2 Answers 6 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - centre `(0,5/4)` and area `= (3sqrt(3))/(4) - pi/3`

5 views Answered 2023-02-05 15:29