1. ### Points on either side of a line

Summary:: The set of values of ##b## for which the origin and the point ##(1, 1)## lie on the same side of the straight line ##a^2x+aby+1=0## ##\forall~a\in\mathbb{R},~b>0##. (a) ##a\geq1## or ##a\leq-3## (b) ##a\in~(-3,~0)\cup(\frac13,~1)## (c) ##a\in~(0,~1)## (d) ##a\in~(-\infty,~0)## I...
2. ### B Correlation between shifting graph of a function and shifting the axes

1.To shift the graph of a function : Vertical Shifts : ## y=f(x) +h## where the graph shifts ##k## units up if ##k## is positive and downwards when ##k## is negative. Horizontal Shifts : ##y=f(x+h)## where the graph shifts to the left by ##h## units when positive and to the right when ##h## is...
3. ### What is the reason behind alternate answers to a locus problem.

The problem : A variable line, drawn through the point of intersection of the straight lines ##(x/a)+(y/b) = 1## and ##(x/b)+(y/a)=1##, meets the coordinate axes in A & B . We have to Show that the locus of the mid point of AB is the curve ##2xy(a + b) = ab(x + y)##. The solution : Let ##(h...
4. ### Formulas for Rotation and Translation

Given the coordinates ##P = (3,4)## , find the coordinates of ##P"(x',y')## when the origin is shifted to (1, –2), and the axes are rotated by 90° in the clockwise direction. I attempted to solve this problem using the following formulas : ##x = X + h## and ##y = Y + k## for translation of the...
5. ### Equation of a plane perpendicular to another plane

Hi, I am really stuck!! I need to find the equation of the plane through the line x=2y=3z perpendicular to the plan 5x+4y-3z=8. Can anyone give me any pointers of where to start with this? Not expecting a full solution, just an idea of where to start. THanks!
6. ### Circle and a line dividing the circumference

Homework Statement The line "4x + 3y -4=0 " divides the circumference of circle centred at (5,3) in ratio 1:2.whats the equation of the circle Homework Equations 2πr Distance of a line from point Radius of general circle The Attempt at a Solution I tried finding the distance of the centre...
7. ### Geometry Alternative to SL Loney's Coordinate Geometry

Hello In India, SL Loney's Elements of Coordinate Geometry is very popular for entrance examinations. I wanted to refresh my coordinate geometry, so tried reading through the book. But I found that the language used is old. I found myself referring to current material on the topic to properly...
8. ### Tangent line and normal on a parabola

Homework Statement If the normal at P(ap^2 ,2ap) to the parabola y^2 = 4ax meets the curve again at Q(aq^2, 2aq), show that p^2 +pq+2=0 Homework Equations Point-slope form The Attempt at a Solution I tried putting y=2aq and x=aq^2 but I can seem to simplify the whole thing other than...
9. ### A permutation and combination problem

.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is (1) 901 (2) 861 (3) 820 (4) 780 my attempt: for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
10. ### Geometry Textbook on Co-ordinate Geometry and Vector Analysis

Could you suggest me any textbook on Co-ordinate Geometry and Vector Analysis?
11. ### If two vertices of a square on the same side AB are A(1,2) and B(2,4)...

Homework Statement If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D? Homework Equations 1. y-y1 = m ( x-x1) 2. m=y1-y2 / x1-x2 3. m1*m2= -1 4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2) 5. m=tanA 6. If ax+by+c=0 then its parallel line is ax+by+k=0 The Attempt...
12. ### Equation of ellipse

Find the equation of the ellipse whose eccentricity is 2/3 and which has (2,0) and x+y=0 for focus and corresponding directrix . given answer: (x-2)^2 + y^2 = 4/9 ( ( (x+y)/√2)^2) what i tried doing:- ae=2 ⇒a*2/3=2 ∴a=3 found b=√5. what to do next? please help.
13. ### Tangent to ellipse also tangent to circle

Homework Statement if the tangent at a point P("theta") on the ellipse 16 (x^2) + 11 (y^2) = 256 is also tangent to the circle (x^2) + (y^2) + 2(x) = 15 then ("theta") = ?? 2. The attempt at a solution {{{{ i have taken "theta" as "d" }}}} P [4 cos d , (16/(sqrt11)) sin d] equation of...