Q. 45.0( 2 Votes )

**At what point **

**Answer :**

**Given, equation x ^{2} + xy – 3x + 2 = 0**

Let’s assume that the origin is shifted at point (p, q).

To find: The shifted point (p, q) satisfying the question’s conditions.

We know that, when we transform origin from (0, 0) to an arbitrary point (p, q), the new coordinates for the point (x, y) becomes (x + p, y + q), and hence an equation with two variables x and y must be transformed accordingly replacing x with x + p, and y with y + q in original equation.

Since, origin has been shifted from (0, 0) to (p, q); therefore any arbitrary point (x, y) will also be converted as (x + p, y + q).

The New equation hence becomes:

= (x + p)^{2} + (x + p)(y + q) – 3(x + p) + 2 = 0

= x^{2} + p^{2} + 2px + xy + py + qx + pq – 3x – 3p + 2 = 0

= x^{2} + xy + x(2p + q – 3) + y(q – 1) + p^{2} + pq – 3p – q + 2 = 0

For no first degree term, we have 2p + q - 3 = 0 and p – 1 = 0, and for no constant term we have p^{2} + pq – 3p - q + 2 = 0.

Solving these simultaneous equations we have p = 1 and q = 1 from first equation. And, p = 1 and q = 1 satisfies p^{2} + pq – 3p - q + 2 = 0.

Hence, the point to which origin must be shifted is (p, q) = (1, 1).

**Rate this question :**

**How useful is this solution?We strive to provide quality solutions. Please rate us to serve you better.**

**Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic ExpertsDedicated counsellor for each student24X7 Doubt ResolutionDaily Report CardDetailed Performance Evaluationview all courses**

**RELATED QUESTIONS :**

**What does the ****RD Sharma - Mathematics**

**What does the ****RD Sharma - Mathematics**

**Verify that th****RD Sharma - Mathematics**

Verify that the aRD Sharma - Mathematics

**Find, what the****RD Sharma - Mathematics**

**At what point ****RD Sharma - Mathematics**

**Find what the ****RD Sharma - Mathematics**

Find a point on tRD Sharma - Mathematics

Find the distanceRD Sharma - Mathematics

Find the coordinaRD Sharma - Mathematics