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Syllabus

the number of integral points that lie exactly in the interior of the triangle with vertices (0,0),(0,21),(21,0) is

The base of an equilateral triangle with side 2

alies along theyy-axis such that the mid point of the base is at the origin. Find vertices of the triangle.A straight line through the origin O meets the parallel lines 4x+2y =9 and 2x+y+6=0 at points P and Q respectively, then point O divides the line segment pq in the ratio _

If x

_{1}, x_{2}, x_{3}as well as y_{1}, y_{2}, y_{3}are in G.P. with same common ratio (not equal to 1) then the points (x_{1},y_{1}) , (x_{2},y_{2}), and (x_{3},y_{3}).a. lies on straight line

b. lie on an ellipse

c. lie on a circle

d. are the vertices of a triangle

Please explain brieflyin triABC side AB has the eqn 2x+3y=29 and sideAC has the eqnx+2y=16.if the midpt of BC is (5,6) then eqn of BC is

The diagonals of a parallelogram PQRS are along the lines x+3y=4 and 6x-2y=7. Then PQRS is aA) Rectangle B) Square C) Cyclic Quadrilateral D) RhombusThe answer is option 'D' but my doub't is why can't it be square.please explain it as fast as u can my exam is with in four days

^{o}with the positive direction of y-axis. Then find the equation of the line.Find number of straight lines passing through (2,4) and forming a triangle of 16 Sq. cm with Co ordinate axes

All the points lying inside the triangle formed by the points (1,3), (5,6) amd (-1,2) satisfy:

a)3x+2y_ 0 b) 2x+y+1_0 c) -2x+11_0 d)2x+3y-12_0

^{2}) falls inside the angle made by the lines 2y=x, x>0 and y=3x,x>0 ,then set of values of alpha isSuppose f (x, y)=0 is the equation of the circle such that f(x, 1)=0 has equal roots(each equal to 2) and f (1, x)=0 also has equal roots (each equal to 0). Find the equation of the circle. Thanks !

find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis??

A man starts from the point P (-3,4) and will reach the point Q (0,1) touching the line 2x+y=7 at R. Find R on the line so that he will travel in the shortest distance.(ONURGENTBASIS)

A triangle has lines y=mx1 and y=mx2 as two of its sides where m1 and m2 are the roots of bx^2 + 2hx + a = 0. If P(a,b) is the orthocentre of the triangle then prove that the equation of its third side is (a+b)(ax+by) = ab(a+b-2h)

find the equations to the diagonals of the rectangle the equations of whose sides are x=a, x=a',y=b,y=b'.

thee distance of the point (2,3) from the lne 2x-3y+9=0 measured along a line x-y+1=0 is

one of the bisector of the angle between the lines a(x-1)²+2h(x-1)(y-2)+b(y-2)² =0 is

x+2y-5 = 0 the other bisector is ??answer is 2x-y =0explain ??

Q. Prove that the angle between the lines joining the origin to the points of intersection of the line y=3x+2 with the curve x

^{2}+2xy+3y^{2}+4x+8y=11 is tan^{-1}(2sqrt(2)/3).find the area of triangle formed by the lines y^2-9xy+18x^2=0 and y=9

Find the equation of the st. line bisecting the segment joining the points (5,3) and (4,4) and making an angle of 45 with the x-axis

What is the image of the point (1, 3) in the line x+y-6=0? Thanks!

If the line y = (3)

^{1/2}x cuts the curve x^{3}+ y^{2}+3x^{2}+9 =0 at the points A,B,C, then OA.OB.OC(Obeing origin) equalsa. 36

b. 72

c. 108

d. n.o.t.

Explain brieflyIn an isosceles triangle OAB, O is the origin and OA=OB=6. the equations of the side AB is x-y+1=0 Then the area of the triangle is_

Let L1 be a st line passing through the origin and L2 be the st line x+y=1. If the intercepts made by the circle xsquare + y square-x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1?

a)x+y=0 b) y-x=0 c)x+7y=0 d)x-7y=0

find the equation the of the line parallel to y-axis and drawn through the points of intersection of the lines x-7y+5=0 and 3x+y=0

the no. of lines that are parallel to 2x+6y-7=0 and have an intercept 10 between the coordinate axes is

^{th}of the area of the triangle is what?frrom (1,4) you travel 5root2 units by making 135degree with positive x-axis(anticlockwise) and then 4 units by making 120degree with positive x-axis clockwise to reach Q.find coordinate of point Q

Pls solve this question and explain me clearly what is locus

If the equation of the lous of a point equidistant from the points (a1, b1) and (a2,b2) is (a1-a2)x+ (b1-b2)y+c=0 then find the value of c.

An equilateral triangle has a centroid at the origin and one side is x+y=1. The equation of the other sides are_______.

the perpendicular from origin to the line y=mx+c meets at the point (-1,2).find m and c?

The area of the quadrilateral formed by y =1 -x, y =2 -x and the coordinate axes is

a. 1

b. 2

c. 3/2

d. n.o.t.

A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at the points P and Q respectively.

When O is the origin, find the minimum value of OP + OQ, as L varies ?