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Co-ordinate Geometry.
by dhwani bhatt - Monday, 11 June 2012, 10:20 PM
  TG Sir , Please help me with the below mentioned questions.

1)Find the equation of lines which cut off intercepts on the axis whose sum and product are 1 and -6 respectively ?

2)Find the lines through the point (0,2) making angles (pi/3) and (2pi/3) with the X-axis . Also find the lines parallel to them cutting the Y-axis at a distance of 2 units below the origin ?

3) The Co-ordinates of the vertices of the triangle are (7,2) (5,-2) (-1,0). What will be the co-ordinate of orthocentre of a Triangle ?

4)If y=2x*x-mx+3 cuts the X-axis in two distinct point, what will be the value of m ?

5)Ramesh drives his alto along the line y=(root3)x from the origin. If the speed of car is 10m/s and he drives for 2 seconds, then find the co-ordinates (x1,x2) of the point where he stops (x1,x2 >0) ??
Re: Co-ordinate Geometry.
by TG Team - Tuesday, 12 June 2012, 02:12 PM
 

Hi Dhwani smile

1. A line which lines makes intercept a and b at X-axis and Y-axis respectively has an equation: x/a + y/b = 1

According to given condition, we have a + b = 1 and ab = -6 clearly (a, b) ≡ (3, -2) or (-2, 3). So the two lines are x/3 - y/2 = 1 => 2x - 3y - 6 = 0 AND -x/2 + y/3 = 1 => 3x - 2y + 6 = 0.

4. y = 2x² - mx + 3 represents an upward parabola. It will cut X-axis in two distinct points if discriminant of the quadratic expression is > 0.

That is, m² - 4(2)(3) > 0

=> m² > 24 i.e. m > 2√6.

All questions are based on basic co-ordinate for which I'd recommend you to go through any 11-12th std text book.

Kamal Lohia 

Re: Co-ordinate Geometry.
by dhwani bhatt - Tuesday, 12 June 2012, 10:13 PM
  Thanks a lot sir.

Please help me with the rest questions also. I tried my mettle , but unable to solve it.