Normals `A O ,AA_1a n dAA_2` are drawn to the parabola `y^2=8x` from the point `A(h ,0)` . If triangle `O A_1A_2` is equilateral then the possible value of `h` is 26 (b) 24 (c) 28 (d) none of these

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

Tongent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the x-axis at point Ba n dD , respectively. If the rectangle A B C D is completed, then the locus of C is y=2a (b) y+2a=c x=2a (d) none of these

If normals drawn at three different point on the parabola y^(2)=4ax pass through the point (h,k), then show that h hgt2a .

The set of points on the axis of the parabola (x-1)^2=8(y+2) from where three distinct normals can be drawn to the parabola is the set (h ,k) of points satisfying (a)h >2 (b) h >1 (c)k >2 (d) none of these

The area of the triangle formed by the tangent and the normal to the parabola y^2=4a x , both drawn at the same end of the latus rectum, and the axis of the parabola is 2sqrt(2)a^2 (b) 2a^2 4a^2 (d) none of these

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n^2=0,n in Zdot If the two circles have exactly two common tangents, then the number of possible values of n is 2 (b) 8 (c) 9 (d) none of these

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these