Mathematics - Coordinate Geometry - II
Exam Duration: 45 Mins Total Questions : 30
The equation of the parabola having vertex at(0,1) and the focus at(0,0), is
- (a)
\(x^2=4(y-1)\)
- (b)
\(x^2=-4(y-1)\)
- (c)
\(x^2=4(y+1)\)
- (d)
\(x^2=-4(y+1)\)
The equation of the matrix of the parabola\(y^2+4y+4x+2=0\) is
- (a)
x=-1
- (b)
x=1
- (c)
\(x=-\frac { 3 }{ 2 } \)
- (d)
\(x=\frac { 3 }{ 2 } \)
The curved is represented by the parametric equations x=t2+t+1,y=t2-t+1 is
- (a)
a pair of straight lines
- (b)
a circle
- (c)
a parabola
- (d)
an ellipse
If lengths of the focal chord segments of the parabola y2=4ax are l1 and l2,then length of the latus rectrum is
- (a)
\(l1+l2\over2\)
- (b)
\(4 l1l2\over l1+l2\)
- (c)
\(2 l1l2\over l1+l2\)
- (d)
\(\sqrt { l1l2 } \)
The coordinates of the focus of the parabola y2=8x are
- (a)
(2,0)
- (b)
(-2,0)
- (c)
(0,2)
- (d)
(0.-2)
The equation of the normal to the parabola x2 =4y through point (1,2) is
- (a)
2x+y-4=0
- (b)
4x-3y+2=0
- (c)
2x-y=0
- (d)
None of these
If (2,0) is the vertex and y axis the directrix of a parabola,then its focus is
- (a)
(2,0)
- (b)
(-2,0)
- (c)
(4,0)
- (d)
(-4,0)
The staright line y = 2x+c touches the parabola y2 =8x; then value of c is
- (a)
1
- (b)
2
- (c)
3
- (d)
4
Equation of the normal to the parabola y2 =4ax at the point (at2,2at),is
- (a)
ty=x+at2
- (b)
tx=y+at2
- (c)
y= -tx+2at+at3
- (d)
None of these
The equation of the common tangent touching the circle (x-3)2 + y2 =9 and the parabola y2 =4x above the x-axis,is
- (a)
\(\sqrt3y=3x+1\)
- (b)
\(\sqrt3y=-(x+3)\)
- (c)
\(\sqrt3.y=x+3\)
- (d)
\(\sqrt3y=-(3x+1)\)
The condition that the chord of the parabola y2 =4ax whose midpoint is (x1,y1) should subtend a right angle at the vertex, is
- (a)
y12 -2ax1+8a2=0
- (b)
y12 -ax1+8a2=0
- (c)
y12 -2ax1+7a2=0
- (d)
y12 -ax1+5a2=0
If the segment of the line lx+my+n =0 intercepted by the parabola y2 =4ax, subtends a right angle at the vertex ,then
- (a)
al+n=0
- (b)
4am+n=0
- (c)
4al+4am+n=0
- (d)
4al+n=0
The angle between the pair of tangents drawn from the point (1,2) to the ellipse 3x2+2y2=5 is
- (a)
\(tan^{-1}({{6\sqrt5}\over 5})\)
- (b)
\(tan^{-1}({{3\sqrt5}\over 5})\)
- (c)
\(tan^{-1}({{12\sqrt5}\over 5})\)
- (d)
None of these
The eccentricity of an ellipse whose pair of a conjugate diameters are y=x and 3y=-2x is
- (a)
\(2\over3\)
- (b)
\(1\over3\)
- (c)
\(1\over \sqrt3\)
- (d)
None of these
The foci of the ellipse 25(x+1)2 +9 (y+2)2 =225 are
- (a)
(-1,2) and (-1,-6)
- (b)
(-2,1) and (-2,6)
- (c)
(-1,2) and (-1,-6)
- (d)
(-1,-2) and (-2,-1)
The equation \({x^{2}\over a-4}+{y^{2}\over 6-a}=1\) ,represents an ellipse if
Locus of the point of intersection of the perpendicular tangents to an ellipse is
- (a)
a straight line
- (b)
a circle
- (c)
an ellipse
- (d)
a hyperbola
When m varies ,the locus of the point of intersection of the straight lines \({x\over a}+{y\over b}=m\) and \({x\over a}-{y\over b}={1\over m}\) is a
- (a)
parabola
- (b)
ellipse
- (c)
hyperbola
- (d)
circle
The line lx+my+n=0 is tangent t other hyperbola \({x^{2}\over a^{2}}-{y^{2}\over b^{2}}=1\)
- (a)
a2l2+b2m2=n2
- (b)
a2l2-b2m2=n2
- (c)
am2+b2n2=a2l2
- (d)
None of these
If x=9 is the chord of contact of the hyperbola x2-y2=9 ,then equation of the corresponding pair of tangents is
- (a)
9x2-8y2+18x-9=0
- (b)
9x2-8y2-18x+9=0
- (c)
9x2-8y2-18x-9=0
- (d)
9x2-8y2+18x+9=0
The line x + y = 1 meets the lines represented by the equation y3 - 6xy2 + 11x2y - 6x3 = 0 at the points P, Q, R. If O is the origin, then (OP)2 + (OQ)2 + (OR)2 is equal to
- (a)
\(\frac{85}{72}\)
- (b)
\(\frac{121}{72}\)
- (c)
\(\frac{211}{72}\)
- (d)
\(\frac{217}{72}\)
The pair of straight lines joining the origin to the common points of x2 + y2 = 4 and y = 3x + c are perpendicular, if c2 is equal to
- (a)
20
- (b)
13
- (c)
1/5
- (d)
5
Mixed term xy is to be removed from the general equation of second degree ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, one should rotate the axes through an angle \(\theta\) then tan 2\(\theta\) equal to
- (a)
\(\frac { a-b }{ 2h } \)
- (b)
\(\frac { 2h }{ a+b } \)
- (c)
\(\frac { a+b }{ 2h } \)
- (d)
\(\frac { 2h }{ a-b } \)
Type of quadrilateral formed by the two pairs of lines 6x2 - 5xy - 6y2 = 0 and 6x2 - 5xy - 6y2 + x + 5y - 1 = 0 is
- (a)
square
- (b)
rhombus
- (c)
parallelogram
- (d)
rectangle
Two pairs of straight lines have the equations y2 + xy - 12x2 = 0 and ax2 + 2hxy + by2 = 0. One line will be common among them, if
- (a)
a = - 3(2h + 3b)
- (b)
a = 8(h - 2b)
- (c)
a = 2(b + h)
- (d)
a = - 3(b + h)