JEE Advanced Mathematics: Coordinate Geometry Practice Questions

11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Find the equation of a line with slope 2 and y-intercept 3.$
Easy
Q2.
$W ha t i s t h ece n t er o f t h ec i r c l e g i v e nb y t h ee q u a t i o n (x - 1)^{2} + (y + 2)^{2} = 9 ?$
Easy
Q3.
$Find the midpoint of the line segment joining (0, 0) and (4, 8).$
Easy
Q4.
$A circle passes through the origin and has its center on the line y = x. If it also passes through the point (2, 0), find the equation of the circle.$
Medium
Q5.
$The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is:$
Medium
Q6.
$I f t h e l in ey = m x + 1 i s a t an g e n tt o t h e p a r ab o l a y^{2} = 4 x, t h e n t h e v a l u eo f mi s :$
Medium
Q7.
$I f t h e l in ey = m x + c i s an or ma l t o t h ee l l i p se x^{2} / a^{2} + y^{2} / b^{2} = 1, t h e n c^{2} i se q u a l t o :$
Hard
Q8.
$T h e l oc u so f t h e mi d p o in t o f t h ec h or d so f t h ec i r c l e x^{2} + y^{2} = 4 w hi c h s u b t e n d anan g l eo f 120 d e g r ees a tt h ece n t er i s a c i r c l e . F in d t h er a d i u so f t hi sc i r$
Hard
Q9.
$A v a r iab l ec h or d o f t h e p a r ab o l a y^{2} = 4 a x s u b t e n d s a r i g h t an g l e a tt h e v er t e x . I f t h ec h or d p a sses t h r o ug ha f i x e d p o in t (h, 0), f in d t h e v a l u eo f h .$
Hard
Q10.
$L e tt h ec i r c l e x^{2} + y^{2} = 9 in t er sec tt h e h y p er b o l a x y = 4 a t f o u r p o in t s . I f t h e p r o d u c t o f t h es l o p eso f t h e l in es j o inin g t h ese p o in t s t o t h eor i g ini s k, f$
Hard
Q11.
$T h e l oc u so f t h e p o in t o f in t er sec t i o n o f t h e t an g e n t s t o t h e h y p er b o l a x^{2} / a^{2} - y^{2} / b^{2} = 1 w hi c hmak e anan g l e a l p ha w i t h e a c h o t h er i s :$
Hard

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