JEE Main Mathematics — Coordinate Geometry previous year questions with solutions.
Let $A={(x,y)\in R\times R\mid 2{x}^{2}+2{y}^{2}-2x-2y=1}$ $B={(x,y)\in R\times R\mid 4{x}^{2}+4{y}^{2}-16y+7=0}$ and $C={(x,y)\in R\times R\mid {x}^{2}+{y}^{2}-4x-2y+5\leq {r}^{2}}$. Then the minimum value of $|r|$ such that $A\cup B\subseteq C$ is equal to
Let the points of intersections of the lines $x-y+1=0,x-2y+3=0$ and $2x-5y+11=0$ are the mid points of the sides of a triangle $\mathrm{ABC}.$ Then the area of the triangle $\mathrm{ABC}$ is
The intersection of three lines $x-y=0,x+2y=3$ and $2x+y=6$ is a/an
Let $P$ be a variable point on the parabola $y=4{x}^{2}+1.$ Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y=x$ is:
For the four circles $M,N,O$ and $P,$ following four equations are given: Circle $M:{x}^{2}+{y}^{2}=1$ Circle $N:{x}^{2}+{y}^{2}-2x=0$ Circle $O:{x}^{2}+{y}^{2}-2x-2y+1=0$ Circle $P:{x}^{2}+{y}^{2}-2y=0$ If the centre of circle $M$ is joined with centre of the circle $N,$ further centre of circle $N$ is joined with centre of the circle $O,$ centre of circle $O$ is joined with the centre of circle $P$ and lastly, centre of circle $P$ is joined with centre of circle $M,$ then these lines form the sides of a
Let $P$ and $Q$ be two distinct points on a circle which has center at $C(2,3)$ and which passes through origin $O.$ If $OC$ is perpendicular to both the line segments $CP$ and $CQ,$ then the set ${P,Q}$ is equal to
Let $A(-1,1),B(3,4)$ and $C(2,0)$ be given three points. A line $y=mx,m>0$ , intersects lines $AC$ and $BC$ at point $P$ and $Q$ respectively. Let ${A}_{1}$ and ${A}_{2}$ be the areas of $\Delta ABC$ and $\Delta PQC$ respectively, such that ${A}_{1}=3{A}_{2}$, then the value of $m$ is equal to :
The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S(>R)$ respectively from the origin, is :
The locus of mid-points of the line segments joining $(-3,-5)$ and the points on the ellipse $\frac{{x}^{2}}{4}+\frac{{y}^{2}}{9}=1$ is :
Let the equation ${x}^{2}+{y}^{2}+px+(1-p)y+5=0$ represent circles of varying radius $r\in (0,5].$ Then the number of elements in the set $S=${$q:q={p}^{2}$ and $q$ is an integer} is ___________
The equation of one of the straight lines which passes through the point $(1,3)$ and makes an angles ${\mathrm{tan}}^{-1}(\sqrt{2})$ with the straight line, $y+1=3\sqrt{2}x$ is
A square $ABCD$ has all its vertices on the curve ${x}^{2}{y}^{2}=1.$ The midpoints of its sides also lie on the same curve. Then, the square of area of $ABCD$ is
Let an ellipse $E:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1,{a}^{2}>{b}^{2}$, passes through $(\sqrt{\frac{3}{2}},1)$ and has eccentricity $\frac{1}{\sqrt{3}}$. If a circle, centered at focus $F(\alpha ,0),\alpha >0$, of $E$ and radius $\frac{2}{\sqrt{3}}$, intersects $E$ at two points $P$ and $Q$, then $P{Q}^{2}$ is equal to :
Choose the correct statement about two circles whose equations are given below: ${x}^{2}+{y}^{2}-10x-10y+41=0$ ${x}^{2}+{y}^{2}-22x-10y+137=0$
Let a point $P$ be such that its distance from the point $(5,0)$ is thrice the distance of $P$ from the point $(-5,0).$ If the locus of the point $P$ is a circle of radius $r,$ then $4{r}^{2}$ (in the nearest integer) is equal to __________.
Let $A$ be the set of all points $(\alpha ,\beta )$ such that the area of triangle formed by the points $(5,6),$ $(3,2)$ and $(\alpha ,\beta )$ is $12$ square units. Then the least possible length of a line segment joining the origin to a point in $A,$ is :
Consider a circle $C$ which touches the $y-$ axis at $(0,6)$ and cuts off an intercept $6\sqrt{5}$ on the $x-$ axis. Then the radius of the circle $C$ is equal to :
In the circle given below, let $OA=1$ unit, $OB=13$ unit and $PQ\perp OB$. Then, the area of the triangle $PQB$ (in square units) is :
Let the circle $S:36{x}^{2}+36{y}^{2}-108x+120y+C=0$ be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, $x-2y=4$ and $2x-y=5$ lies inside the circle $S,$ then:
Let ${S}_{1}:{x}^{2}+{y}^{2}=9$ and ${S}_{2}:(x-2{)}^{2}+{y}^{2}=1$. Then the locus of center of a variable circle $S$ which touches ${S}_{1}$ internally and ${S}_{2}$ externally always passes through the points :
The locus of a point, which moves such that the sum of squares of its distances from the points $(0,0),(1,0),(0,1)(1,1)$ is $18$ units, is a circle of diameter $d.$ Then ${d}^{2}$ is equal to
Let $A(1,4)$ and $B(1,-5)$ be two points. Let $P$ be a point on the circle ${((x-1))}^{2}+{(y-1)}^{2}=1$, such that ${(PA)}^{2}+{(PB)}^{2}$ have maximum value, then the points, $P,A$ and $B$ lie on
If the variable line $3x+4y=\alpha$ lies between the two circles $(x-1{)}^{2}+(y-1{)}^{2}=1$ and $(x-9{)}^{2}+(y-1{)}^{2}=4,$ without intercepting a chord on either circle, then the sum of all the integral values of $\alpha$ is
Let the lengths of intercepts on $x$ -axis and $y$ -axis made by the circle ${x}^{2}+{y}^{2}+ax+2ay+c=0,$ $(a<0)$ be $2\sqrt{2}$ and $2\sqrt{5}$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line $x+2y=0,$ is equal to :