Explore topic-wise InterviewSolutions in Class 11.

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your Class 11 knowledge and support exam preparation. Choose a topic below to get started.

1.

If the locus of the point which moves so that the difference (p) 0 of its distance from the points `(5, 0) and (-5,0)` is 2 is `x^2/a^2-y^2/24=1` then a isA. `x^(2)-24y^(2)=1`B. `24x^(2)-y^(2)=24`C. `x^(2)-24y^(2)=24`D. `24x^(2)-y^(2)=1`.

Answer» Correct Answer - B<br>
2.

If the parabola `y^(2)=4ax` passes through the point (2,-3) then find the co-ordinates of the focus and the length of latus rectum.

Answer» Correct Answer - Focus `((9)/(8),0)`, latus rectum `=(9)/(2)`<br>
3.

Find the vertex, focus, axis , latus rectum and directrix of the parabola `y^(2)+4x+6y+17=0`

Answer» Equation of parabola<br> `y^(2)+4x+6y+17=0`<br> `rArr" "y^(2)+6y+9=-4x-17+9`<br> `rArr" "(y+3)^(2)=-4(x+2)`<br> `rArr" "Y^(2)=-4X`<br> Comparing with `Y^(2)=-4aX`<br> 4a=4<br> `rArr" "a=1`<br> Vertex A = (0,0)<br> `rArr" "X=0,Y=0`<br> `rArr" "x+2=0,y+3=0`<br> `rArr" "x=-2,y=-3`<br> `:.` Co-ordinates of vertex = (-2,-3).<br> Focus X = -a,Y=0<br> `rArr" "x+2=-1,y+3=0`<br> `rArr" "x=-3,y=-3`<br> `:.` Co-ordinates of focus = (-3, -3).<br> Equation of axis Y=0<br> `rArr" "y+3=0`.<br> Equation of directrix X=a<br> `rArr" "x+2=1`<br> `rArr" "x+1=0`<br> Length of latus rectum = 4a = 4.
4.

Find the equation of a parabola whose focus and vertex are (0, 0) and (0, 2) respectively.

Answer» The focus (0,0) and vertex (0,2), of the parabola lie on Y-axis.<br> Produce SA + AZ<br> =2+2=4<br> Draw a perpendicular ZM from Z to the axis of parabola. ZM is the directrix of the parabola whose equation is y-4=0.<br> Let P(x,y) be any point on the parabola.<br> Now the equation of parabola<br> PS=PM<br> `sqrt((x-0)^(2)+(y-0)^(2))=y-4`<br> `rArr" "x^(2)+y^(2)=(y-4)^(2)`<br> `rArr" "x^(2)+y^(2)=y^(2)-8y+16`<br> `rArr" "x^(2)=-8(y-2)`.<br>