Question 1 :
The equation of the parabola whose vertex is at (2, -1) and focus at (2, -3) is
Question 2 :
An equilateral triangle is inscribed in the parabola y<sup>2</sup> = 4ax with one vertex at the origin. The radius of the circum circle of that triangle is
Question 3 :
The equation of the tangent to the parabola {tex} y = x ^ { 2 } - x {/tex} at the point where {tex} x = 1 , {/tex} is
Question 4 : The number of point(s) outside the hyperbola <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749c04f511820358e67e9d' height='43' width='79' > form where two perpendicular tangents can be drawn to the hyperbola is/are:
Question 5 : If PCP' and DCD' be a pair of conjugate diameter of an ellipse <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7499c6f511820358e67c11' height='47' width='79' > whose centre is C then (CP)<sup>2</sup> + (CD)<sup>2</sup> equals.
Question 6 :
The tangent at the point A(12, 6) to a parabola intersects its directrix at the point B(-1, 2). The focus of the parabola lies on x-axis. The number of such parabolas is-
Question 7 :
If a circle makes intercepts of length 5 and 3 on two perpendicular lines, then the locus of the centre of the circle is
Question 8 :
The point on the curve y<sup>2</sup> = 4x which is nearest to (2, 1) is
Question 9 :
If cos α = 2/3, then range of the values of φ for which the point φ on the ellipse x<sup>2</sup> + 4y<sup>2</sup> = 4 falls inside the circle x<sup>2</sup> + y<sup>2</sup> + 4x + 3 = 0 is:
Question 10 :
PA and PB are the tangents drawn to y<sup>2</sup> = 4x from point P. These tangents meet the y-axis at the points A<sub>1</sub> and B<sub>1</sub> respectively. If the area of triangle PA<sub>1</sub> B<sub>1</sub> is 2 sq. units, then locus of 'p' is-
Question 11 :
If for the ellipse $\frac{x^{2}}{\alpha^{2}} + \frac{y^{2}}{b^{2}} = 1$, y-axis is the minor axis and the length of the latusrectum is one half of the length of its minor axis, then its eccentricity is
Question 12 :
<font>The point on the curve y</font><sup><font>2</font></sup><font> = 4x which is nearest to (2, 1) is</font></p>
