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Syllabus

Possible values of thita for which the point (cos thita, sin thita ) lies inside the triangle formed by lines x+y=2, x-y=1 and 6x+2y=square root of 10 are _

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

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)

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.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

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

If A = (2,1) B = (-10,6) then the distance between the orthocentres of triangle HBC and HAC is ?

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

The equation of the line belonging to the family of the lines by 3x+4y+6+k(x+y+2)=0 (where k being a parameter) and situated at the greatest distance from the point (2,3) is??

^{2}– 4xy + y^{2}= 0 together with the line x + y + 4root 6 = 0 form a triangle which is what?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

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

^{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??

find the area of triangle formed by the lines y^2-9xy+18x^2=0 and y=9

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 brieflythe lines joining the origin to the points of intersection of x²+y²+2gx+c=0 and x²+y²+2fy-c=0 are at the right angle is ??

answer is g²-f² =c explain??

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).Q. Find the equation of two straight lines which pass through the point(4,5) and make equal angles with two straight lines given by the equations 3x-4y-7=0 and 12x-5y+6=0

How many arrangements can be made with the letters of the word MATHEMATICS if (1) Vowles occur together (2) M is at both Extremes.

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

1.4

2.3

3.2

4.1

In 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_

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 ?

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

Please reply soon .

Thank you .

x-2y+2=0

x+y=0 and

x-y-PI=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

"WHEN THE ORIGIN IS SHIFTED TO THE POINT (2,3) THE TRANSFORMED EQUATION OF THE CURVE IS Xsquare+3xy-2y square+17x-16xy+17y square=225 find the qriginal equatio of the curve"

Please tell the condition in the determinant form also if it is there .

Please help soon .

Thank You .

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?16. If the equation of the pair of straight lines passing through the (1, 1), one making an angle $\mathrm{\theta}$ with the positive direction of x-axis and the other making the same angle with the positive direction of y-axis, is

${\mathrm{x}}^{2}-\left(\mathrm{a}+2\right)\mathrm{xy}+{\mathrm{y}}^{2}+\mathrm{a}\left(\mathrm{x}+\mathrm{y}-1\right)=0,\mathrm{a}\ne -2,\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{sin}2\mathrm{\theta}\mathrm{is}.\phantom{\rule{0ex}{0ex}}\left(\mathrm{a}\right)\mathrm{a}-2\left(\mathrm{b}\right)\mathrm{a}+2\phantom{\rule{0ex}{0ex}}\left(\mathrm{c}\right)2/\left(\mathrm{a}+2\right)\left(\mathrm{d}\right)2/\mathrm{a}$

Find the equation of the line which passes through the point (–4, 3) with slope.

show that the points (3,3),(h,0) and (0,k) are collinear if 1/h+a/k=1/3

^{2}+ y^{2}= 0 is5x

^{2}+ 12xy - 6y^{2}+ 4x - 2y + 3 = 0 and x + ky - 1 = 0 are equally inclined to the x-axis then the value of k is :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.